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THE UNIVERSITY 
OF ILLINOIS 
LIBRARY 


% The 
Frank Hall collection 
of arithmetics, 
presented by Professor 
H. L. Rietz of the 
University of Iowa. 


, LACT 5/3. 
DZEpr 


IMARY 


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LL.D. 


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By CHARLES DAVIE 


oak 


COURSE OF 


MATHEMATICS. 


FULL 


AUTHOR OF A 


SUGGESTIONS. 


| }. Sensible objects should be used in all the elementary opera- 
tions of numbers. 


| 2, The unié of a number, and the number of units taken, should 
be dwelt upon in every example. 


3. The idea of number is purely abstract, and can only be appre- 
hended by the contemplation of sensible objects—individually, and 
collectively. 


4, The eight units of science, arranged into classes in the Tables, | 
| should be carefully distinguished from each other. 


|  §. The idea of the abstract unit, 1, comes from contemplating the | 
| denominate unit, 1 apple. The unit of currency, 1 dollar, is easily 
apprehended; and the foot-rule, or the yard-stick, will fix per- 
inanently in the mind the unit of length. 


| 

| 6. The unit of surface, is the square constructed on the unit of 

| length; and « paper cube, constructed on this square, as a base, 
exhibits to the mind one of the units of volume. The gallon 
measure, and the half-bushel, are two other units of volume in 
common use. 


| 

| 

i 

! 

| 7. The pound, is the most familiar unit of weight, and should be 
exhibited to every class of beginners. The day, is the familiar unit 
of time, and the degree, of angular measure. 


af PREFACE. 


Tue present work is designed for beginners, being 
adapted to the capacities and wants “of very young 
children. M 

It commences with counting, by means of sensible 
| objects, and these are employed through the entire work 
i to illustrate and render familiar the elementary com- 
binations of numbers, 


The work is constructed on the plan of object teach- 
| ing. The object is first presented to the mind, and then 
its number, in connection with other objects of the same 
kind. From these, the child readily passes to the idea 
of number in the abstract, derived as it is, directly, from. 

sensible objects. 


Each Lesson is Bt to illustrate a sing fe rinciple 
31m7T oOmD ti Ae is A} the 1 ssons 1g are 
hr a com OI ; ew r s & +} 


Ala 
= 


’ 


lar pare to be Py sae prrere sto t 
we analysis; afte which, the Table eca. pitula 
been illustra 


Leal 
cc <% 


J 
a 
» 


- 


s. 


PREFACE. 


The subject of Division has been introduced by naming 
the quotients of numbers divisible by 2, 3, 4, &c.; and 
these quotients are not treated as fractions—the term. 
fraction being applied, in abstract nuumbers, only to the 
equal parts of 1, and in denominate numbers, to the equal 
parts of an entire thing, numerically denoted by 1. This 
principle of classification and naming, has not, to my 
knowledge, been used before, and as it forms the basis 
| of a system, is deemed important. 


nn RE ASD 


| The plan of this work requires the beginner to search 

out his way, by short and easy steps, to what lies before 
him. He is to use his faculties to discover principles, 
and not rely on his memory for rules to guide him. 
Hience, the Table is placed at the end of cach Lesson, 
-as the result of what has preceded; and not at the be- 
ginning, as heretofore, in all similar works. 


The combination of the pictorial representation, the 
practical example, and the abstract table, in the order 
in which they are placed, and on pages facing each other, 
has not, I believe, been made before; and I hope it may 
prove a valuable aid in elementary instruction. 


_» The reading of figures is one of the most useful exer- 


, ee in object- De a The Lessons on that subject. 


p-Bnrey toe. te, notie and meet the appre oval ; 


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PRIMARY ARITHMETIC. 


LESSON I. ‘ 


Cranes, can you count? “Vl try, Sister.” 
| Which is your right hand? Which your left? 
Tow many hands Hees you? How many thumbs 
have you on your right hand? How many on 


our left? _ How man, on pele 


o tetie *, ae , 2 
3 ; ave YC re i 
eR F eS 


othe mar Ly "4 a y ony a 

ang y thumb with't fingers, ho 
: ent han ae many on | both? 
_~ How many ears "ai the dog, Carlo? Ho 
| many eyes has How many legs’ | 


6 COUNTING. 


LESSON II. | 


\ y 
Need Dare. 
en eg 


Jane has a few pet rabbits. She is very fond 
of them, and plays with them~*often. They are 
pretty little animals. See how tame and gentle 

_ 24 they are. How many rabbits are there? 
|| Jane feeds them with apples. See how they 
eat. Here are pictures of some apples. | 


” 


How many apples are th 


af? mm 
\ ah val 
‘ ae) 


this row? 


~~. * 


a 


COUNTING. 7 


LESSON ITt. | \s 


1. What isa unit? Ans. A single thin = ‘Bs 


2. What is a number? Ans: AS unit, or a col- 
lection of units. 


3. How may numbers be oxprtsondl Bis, By 

words, by figures, and by letters. 

4, What is counting? Ans. Counting is ex- 
pressing consecutive numbers by words. 


%| 5. How many figures are there? Ans. Ten. 
Name them. RS 


~¥ : : \ 
Naught, One, Two, Three, Four, Five, Six, Seven, Eight, Nine. 


Pees) 4 8 ABR eG 


Count the hats in each of these rows. 


rie renga Nine ) 


Mh A OL to 


den. 


“| Fifteen 


8 COUNTING. 


LESSON IV. 


The ten figures of Arithmetic were first used in 
Arabia. The Arabs are a wandering people, live 
in tents have fine horses and camels. This pic- 
ture will remind you of the country from which 
we got our ten figures. __ 


‘Ten 

\ 
_ Eleven 
elve 


Nineteen ! 


Sixteen = * ; Twenty-five 
Seventeen | Twenty-six 
Eighteen a8: . 7 


% 


COUNTING. 


LESSON V. 


Si AV H 
Sey 
Sy 


. a HENS 4 ‘ 
Sy AN aN SS = S 
NS SN PRN 


SD = WS 
Wy =. LS VE S 
A? <a SS SS 
im SVQ 
elgg AORN 
ee TT. SSNS 
De |e SN bom 
. 3 


Here is a Roman father teaching his son to 
count. The Romans used the seven letters, I, V, | 
X, L, C, D, and M, to express numbers; thus, 


One . Eleven 
Twelve 
hirteen 


10 ADDITION. 


LESSON VI. 


Anpprtion is the operation of finding the sum of 
two or more numbers. 


1. One apple and one apple, are 
how many apples? One and one are how many? 


? 


& 
mA, 


“Q one ap le and two Snide e's Re 
how many ‘apples? One and two are how many ? 


) oe: Ones digs and mat eis are 
PAE hy aw many apples! One and three are how many? 


5. 6 apple and fee beatles are | 
how many apples? One and il are how mes! | 


ADDITION. 11 


i 


1. John has 1 apple in one hand, and 2 apples 
in the other hand; how many apples has he in 
both hands? 1 and 2are how many? 2 and 1? 

2. One apple and 3 apples, are how many 
apples? 1 and 38 are how many? 38 and 1? i 

3. Charles has 1 marble, and James gives him « 
5 marbles; how many marbles will Charles then 
have? 1 and 5 are how many? 5 and 1? 

4, Joseph has 1 chestnut, and William gives 
him 7 chestnuts; how many chestnuts will Joseph 

then have? 1 and 7 are how many? 7 and 1? 
| 5. One orange and 8 oranges, are how many 

oranges? 1 and 8 are how many? 8 and 1? 

6. One lemon and 10 lemons, are how many 
| lemons? 1 and 10 are how many? 10 and 1? 

7. One ball and 9 balls, are how many balls? 
How many arel and 9? 9 and 1? 

8. One pear and 7 pears, are how many pears? 

How many areland 7? 7 and 1? 

9. Nine marbles and 1 marble, are how many ? 

10. James gave 1 cent ae an apple, and 4 cents | 
for an orange; how 


and 

and 8 Y 
1 and 9 are 10 

| *1 -andst0 “ares 21 alia: 


ADDITION. 


LESSON VII. 


1. Two pears and one pear, are 
how many pears? ‘T'wo and one are how many ? 


2. Two pears and two pears, are 
how many pears? Two and two are how many ? 


3. ‘Two pears and = three pears, _— are 
how many pears? Two and three are how many? 


“" We watches * Sande four watches, are 
how 1 m | ski | Two and four are how many? | 


Tne 


™~ . NE oe 


ae “a} ~~ 


| 5. Two watches and five watches, "are 
| how many watches? Two and five are how many? 


ee are eee 


ADDITION. I3 


1. Two pears and 1 pear are how many pears? 
How many are 2 and 1? 1 and 2? 

2. Two pears and 5 pears are how many pears ? 
How many are 2 and 5? 5 and 2? 

3. Two pears and 7 pears are how many pears? 
How many are 2 and 7? 7 and 2% 

4. ‘Two pears and 9 pears are how many pears? 
How many are 2 and 9? 9 and 2? Baty 

5. Two pears and 8 pears are how many pears? 
How many are 2 and 8? 8 and 2? 

6. Two watches and 10 watches are how many | 
watches? 2and10are how many? 10 and 2? 

7. Two watches and 6 watches are how many 
watches? 2 and 6 are how many! 6 and 2? 

8. Two watches and 4 watches are how many 
watches? 2 and 4are how many? 4 and 2? 

9. Two watches and 8 watches are how many 

| watches? 2 and 3 are how many? 3 and 2? 

10. Two watches and 2 watches are how many 
watches? 2 and*2 are how many ¢ | 
11. A pear-tree has 8 pears on one laae, and 9 | 

pears on another limb ; how many pears are there 


2 ae er 40 
2 and 9 are’ yet 
2 and 20: ‘eree19” : 


| 2 and 3 are 5 
2 and 4 are 6 
2 and 5 are E t 


ADDITION. 


LESSON Wirt: 


1B Three ee and one sheep, are 
how many sheep? Three and one are how many? 


| 
| 
| 
7 
| 
| 


2. Three cae and two sheep, are 
| how many sheep? Three and two are how many? 


3. Three ihe and three tenes are 
how many sheep? Three and three are how. many? 


indian Three mortars. and "four TN. are. 
; : mortars! Three and four are how ee 


| 
5. Three mortars and five mortars, ere | | 
how many mortars? Three and five are how many? 


ADDITION. 15 


1. Three sheep and 6 sheep, are how many 
sheep? 3 and 6 are how many? 6 and 3? 
2. Three sheep and 7 sheep, are how many 

sheep? 8 and 7 are how many? 7 and 3? 

3. Three sheep and 8 sheep, are how many 
sheep? 8 and 8 are how many? 8 and 3? 

4, Three sheep and 10 sheep, are how many 
sheep? 3 and 10 are how many? 10 and 3? 

5. Three mortars and 9 mortars, are how many 
mortars? 3 and 9 are how many? 9 and 3? 

6. John has 3 rabbits, and James 7; how many 
rabbits have both of them? 5 and 7 are how 
many? 7 and 5% 

7. John has 3 apples, and Frank gave him 9 
more; how many did he then have? 9 and 3 are 
how many? 8 and 9? | 

8. Reuben’s shoes cost 2 dollars, and his coat | 
cost 8 dollars; how many dollars did both cost? 

9. There are 3 birds on one tree, and 7 on an- 
other; how many birds are there on both trees ? 

10. A grocer sold 3 pounds of tea to one man, 
and J fo to another ; oh many pounds did 


- 3 and 5 are 8 8 and 10 are 13. | 


16 ADDITION. 


LESSON IX. 


4 1. Four bells and one bell, are 
how many bells? Four and one are how many ? 


2. Four bells and two bells, are 
how many bells? Four and two are how many ? 


is 3. Four bells and _ three bells, are 


‘ | how chi bells? Four and three are how ae ? 
| | fhinthhh Poa 
‘4, Fr ut a _and four chairs, are 


) 


5. Four chairs and five chairs, are 
how many chairs? Four and five are how many? 


ried 
ae 
: ; ps 


ADDITION. iby 


1. Four bells and 6 bells, are how many bells? 
4 and 6 are how many? 6 and 4? 

2. Four bells and 8 bells, are how many bells? 
4 and 8 are how many? 8 and 4? , 

3. Four bells and 10 bells, are how many bells? 
4 and 10 are how many? 10 and 4? 

4. Four bells and 9 bells, are how many bells? 
4 and 9 are how many? 9 and 4? : 

5. Four bells and 7 bells, are how many bells? 
4 and 7 are how many? 7 and 4? 

6. A farmer has 4 black cows, and 5 red ones; 
how many cows has he in all? 4 and 5 are how 
many ? 

7. A farmer has 5 sheep in one pasture, and 4 
in another; how many sheep has he in both pas- 
tures ? 

8. A knife costs 8 cents, and a top 4 cents; how 
many cents do both cost? 

9. Jane has 4 cents in one hand, and 9 cents in 
the other; how many cents has she in n bot hands? 

4 and 9 are how many ? Sng | 
0 On ne cat. pes, 4 commas and othe: cat his 6 


~ 


and 8 are: 12 


4 and 9 are 13 
4 and 10 are 14 __ 


18. - ADDITION. 


LESSON X. 


1. Five mugs and one mug, are 
how many mugs? Five and one are how many ? 


2. Five mugs and two mugs, are 
how many mugs? ‘Five and two are how many? 


3. Five mugs and three mugs, are 
how many mugs? Five and three are how many ? 


4. Five axes and ___ four AXCS, vb 
ne: how man ee! Five. and four are how man 


peel 
5; Five axes... and five axes, 


f how many axes? Five and five are how aie 


ata oe 3 


ADDITION. 19 


1. Five mugs and 6 mugs, are how many mugs? 
How many are 5 and 6? 6 and 5? 

2. Five mugs and 8 mugs, are how many mugs? 
How many are 5 and 8? 8 and 5? 

3. Five axes and 9 axes, are how many axes ¢ 
Ylow many are 5 and 9? 9 and 5? 

4. Wive axes and 7 axes, are how many axes? 
How many are5 and 7? 7 and 5? 

5. Five axes and 10 axes, are how many axes? 
How many are 5 and 10? 10 and 5? 

6. A farmer bought 8 lambs at one time, and 5 
at another time; how many did he buy in all? | 

7. Albert spent 5 cents for candy, and 6 cents 
for nuts; how many cents did he spend in all? 5 
and 6 are how many? 6 and 5? 

8. James paid 5 cents for a top, and 10 cents 
for a pencil; how many cents did he pay for both? 

9. A tailor bought 5 yards of cloth, and then 5 
yards more; how many yards did he buy in all? 
5 and 5 are how many? 
10. John gave 5 dollars for his hat, and 9 dol- 
for his coat; how many dollars a Hie bined 


5 it 6 Se: u 

5 and 7 are 12 

' 5 and 8 are 8 5 and 8 are 13 
® and 4 are 9 5 and 9 are 14 

& and 5 are 10 5 and 10 are 15 


20 ADDITION. 


LESSON XI. 
ila Six trees and one tree, are 
how many trees? Six and one are how many? 


a a a ll a las I 


! 
2. Six trees and two trees, are | | 
how many trees? Six and two are how many? | 


8. ©: Six trees and three trees, are | 
how many trees? Six and’ three are how many? 


ADDITION. 21 


oe ee ae 


Riise are 6 trees in one row, and 6 trees in 
ver ; how many trees in both rows ? 
9. Six trees and 7 trees, are how many trees? 
llow many are 6 and 7? 7 and 6? 
3. Six trees and 9 trees, are how many trees ? 
Ilow many are 6 and 9% 9 and 6? | 
| 4. Six trees and 10 trees, are how many trees? | 
_| How many are 6 and 10? 10 and 62. 
| 5. Six trees and 9 trees, are how many trees? | 
How many are 6 and 9% 9 and 6? 

6. Bought a bottle of ink for 8 cents, and some 
pens for 6 cents; how many cents were paid for 
both ? 

7. Andrew, after spending 6 cents, had 8 cents 
left; how many cents had he at first? 0 and 8 

} are bist many? 8 and 6? 

-; 8. Edward missed 6 words in spelling his les- 

_|son, and Henry missed 95 how many words did 
both miss ? a 

9. Maria had 6 flowers, and Susan 7; how 3 
many flowers had both? A Be 
10. gopoets ee 9 sweet eB, and 6 wont ap 


nad he 


< are ‘ UE ey 
BRO BG gh 3 
and 10 are 16 | 


d 
*. ae. 


; 6 and 3 are 
| 6 and 4 are 
x 6 and 5 are 


Ke 


OS oS 
5 i 
<=) 


99, ADDITION. 


LESSON XII. 


Ue Seven boots and one boot, are 
how many boots? Seven and one are how many? 


Ws 


2. Seven boots and two boots, are 


how many boots? Seven and two are how many? | 


N 
‘ 


RNR ome oe 


3. ' Seven trees and_ three trees, are 


how many trees? Seven and three are how many? | 


©8868 06 


_ 8. Seven balls a five ei . 7 
how many balls? ‘Severi and five a are how r 


4 


— 


ADDITION. 93 


1. Seven boots and 6 boots, are how many 
boots? 7 and 6 are how many? 6 and 7? 

2. Seven balls and 8 balls, are how many balls? 
How many are 7 and 8? 8 and 7? 

8. Seven balls and 9 balls, are ig many balls? 
rai many are 7 and 9? 9 and 7 

4, Seven balls and 10 balls, are els many balls? 
How many are 7 and 10? 10 and 7? 

5. Seven balls and 7 balls, are how many balls? 
How many are 7 and 7? 

6. Richard hte 7 lines yesterday, and 5 to- 
day ; how many lines did he write in both days ¢ 

7. If a barrel of sugar costs 7 dollars, and a 
| barrel of flour 8 dollars; how many dollars will 
| both cost? 
| 8. Andrew has 7 rabbits, and James gave him 

8 more; how many rabbits had he then ? 
| 9. John picked 7 quarts of strawberries, and 
James picked 9 quarts; how ae quarts did 
both pick ? . 

10. Howard* earned 7 shillings one week, ssid 

10 shillings pike next week; how many oss a 


T and 9 are 16 
7 and 5 are 12 | and 10 are” AT 


a os 


24 ADDITION, 


LESSON XIII. 


1. Eight little girls and one little girl, are 
how many girls? Eight and one are how many? 


2. Ei ght little girls and _ two little girls, are 
how many girls? Eight and two are how many ? 


3. Right little girls and three little girls, are 
how many girls? Eight and three are how many? 


€9880080 © @ @ © 


5. Hight balls » and 
how many balls? Eight and: 


ADDITION. 25 


1. There are 8 little girls in one row, and 6 in 
another row; how many are there in both rows ? 

2. Eight balls and 8 balls, are how many balls? 
Tow many are 8 and 8? 

3. Eight balls and 9 balls, are how many balls? 
Tiow many are 8 and 9? 9 and 8? 

4. Eight balls.and 10 balls, are how many balls? 
How many are 8 and 10? 10 and 8? 

5. Isaac is 8 years old, and Mary 6 years older; 
how old is Mary ? 
| 6. Bought a ealf for 8 dollars, and a sheep for 6 
| dollars; how many dollars were paid for both ? 
Bae is spelled 8 words, and James 9 words; 
| how many words did both of them spell ? 
; 8. Charles had 8 oranges in one hand, and 4 in 
| the other; how many had he in both hands? 
9. Reuben had 8 cents in one pocket, and 8 in 
j another; how many cents had he in both pockets? 

10. A man had 8 dollars, and borrowed 7 more; 
how many dollars had he then? 
} 11. John has 4 marbles, and won 8 from J ames; | 

how many marbles had he then? 4 and 8 are how 


8 and 9 are 
8 and 10 are © 


ADDITION. |. 


LESSON XIV. 


gaddadeda & 


ie Nine bottles and one bottle, are. 
how many bottles?) Nine and one are how many? } 


Nine bottles and two bottles, are 
how many bottles? Nine and two are how many? 


j beebbeoes dé 


“3. Nine bottles and three bottles, are 
Hihew many bottles? Nine and three are how many? 


fi deine commas 60666 


im. Nine balls and five balls, are 
| how many balls? Nine and five are how many ? 


ADDITION. 


1. Nine bottles and 6 bottles, are how many 
bottles? 9 and 6 are how many? 6 and 9% 

2. Nine bottles and 7 bottles, are how many 
bottles? 9 and 7 are how many? 7 and 9? 

3. Nine balls and 8 balls, are how many balls? 
9 es 8 are how many? 8 and 9? 

4. Nine balls and 9 balls, are how many balls? 
9 and 9 are how many ? 

5. Nine balls and 10 balls, are ion many balls? 
9 and 10 are how many? 10 and 9% 

6. There are 7 trees in one row, and 9 in-an- 
other; how many trees are there in both rows? 
7 nid 9 are how many ? 

7. There are 6 boys sitting on one bench, and 
9 on another; how many boys are there on both 
benches ? 

8. One of Willie’s hens has 9 chickens, aha an- 
other 8; how many chickens has he in all? 9 
and 8 are how many? 8 and 9? 

9. In an orchard there are 9 pear-trees, and 9 
peach-trees; how many trees are there in all? 

10. Ten bottles and 9 bottles, are how many 
bottles? 9 and 10 are how many ? 


9 and 1 are 10 9 and 6 are 15 
9 and. 2 are 11.-|. 9 and 7 are. 16 
9 and 8 are 12 9 and 8 are 17 
9 and 4 are 13 9 and 9 are 18 
9 and 5 are 14 |°'9 and 10: are 19 


28 ADDITION. 


LESSON XY. 


ELE f 


Ten soldiers and  onesoldier, are 
bas many soldiers? Ten and one are how many? 


fopaganaas ff 


Ten soldiers and two soldiers, are |. 
Be many soldiers? Ten and two are how many? 


Saadaidads Aaa 


Ten soldiers and_ three soldiers, are 
ae many soldiers? Ten and three are how many? 


[|—r HO GOO GBG6O8O8 86086 


4, _ Ten balls and four balls, are 
_| how many balls? Ten and four are how many? 


©0808 082880 8680908 


5. Ten balls and five balls, are 
how many balls? Ten and five are how many? 


ADDITION. 29 


1. Ten soldiers and 6 soldiers, are how many 
soldiers? 10 and 6 are how many? 6 and 10% | 

2. Ten soldiers and 7 soldiers, are how many | 
soldiers? 10 and 7 arehow many? Tand10? | 

3. Ten balls and 8 balls, are how many balls? | 
10 and 8 are how many? 8 and 10? | 

4. Ten balls and 9 balls, are how many balls? | 
10 and 9 are how many? 9 and 10? | 

5. Ten balls and 10 balls, are how many balls? | 
10 and 10 are how many ? | 

6. A cat caught 10 mice one day, and 6 the | 
next day ; how many mice did she catch? 10 and 
6 are how many ? 
_ 7. A man bought a saddle for 10 dollars, and a 
bridle for 8 dollars; how many dollars did both 
cost him ? 

8. John has 10 cents in one pocket, and 8 in 
another pocket; how many cents has he in both? 

9. There are 10 doves on the roof of the barn, 
and 9 on the roof of the house; how many doves 
are there in all? 

10. Watson sold 7 oranges, and had 10 left; 
how many oranges had he at first ? 

Ps PR EN hv OI 
10 and 1 are 11 10 and 6 are 16 
10 and 2fare 12 10 and 7 are 17 
10 and 3 are 13 10 and 8 are 18 
9 
0 


10 and 4 are 14 10 and are 19 
10 and 5 are 15 10 and10 are 20° 


2 


ee 


TH OmOPOODW-T H> <> OO H Or bo aT bo Or CS H= CO Sd LO AT CO Gs LO 


ADDITION. 


LESSON 


REViEW 


and 4 are how many ?| 5 


and 2 
and 3 
and 2 
and 5 
and-3 
and 6 
and 7 
and 4 


and 2 
and 3 
and 5 
and 7 
and 4 
and 9 
and 5 
and 8 
and 5 


and 4 
and 5 
and 6 
and 3 
and 2 
and 8 
and 7 
and 4 
and 7 


mv I: 


LESSON. 


and 6 are how many ¢ 


3 and 8 
and 4 ef 
and 9 re 
and 3 Me 
and 8 + 
and 4 re 
and 6 vf 
and 7 4 


H= ~T bO St CH S Or C LO = 09 So aT OD SO OC LC Or > Oo H ATCO DO OO 


and 7 are how many ? 
and 6 < : 


and 3 “ 
and 5 rs 
and 8 bie 
and 6 y 
and 4 : 
and 7% * 
and 2 a 


and 6 are how many? 
and 7 . | 


and.d ee 
and 7 he ee 
and 8 ¥ 
and 9 Ke 
and 8 © * 
and 3 xs 


ander 5, 8 


ADDITION. 


LESSON XVII. 


READING FIGURES. 


Twenty-one 

Twenty-nine . 

Thirty-seven . + 

Forty | 

Sixty-seven 

Seventy va 
Ninety-five . «-. 

One hundred . er. 

One hundred andten. . . . 
One-hundred and seventy-five . 
One hundred and ninety-five 
Two hundred and sixty-seven . 


Three hundred and twenty-seven . 


Three hundred and ninety-five . 
Four hundred and fifty 

‘Your hundred and sixty-seven . 
Five hundred 


Six hundred and seventy-tu oe 


Seven hundred . . . “s ; 


Seven hundred and fiftee “2 os. 


LESSON XVIII. 


_ 82 ADDITION. 
| 
| PROMISCUOUS EXAMPLES. 


1. John bought a top for 6 cents, and some 
eandy for 5 cents; how many cents did he pay 
for both ? 


Awatysis.—He pad yor both as many cents as 
there are in the sum of 6 cents and 5 cents: the 
ei. of 6 and 5 is 11: Therefore, he paid for 
both, 11 cents, 


| 2. In a school-room there are 5 boys on one 
bench, and 9 boys on another; how many boys 
| are there on both benches? 
_ 3. A farmer sold a pig for 10 dollars, and a 
| ¢ calf for 9 dollars; how many dollars did he get 
| for both? 
| 4, James paid 5 cents for an inkstand, and 8 
_cents for pens; how many cents did he pay for 
| both? 
| 5. A tailor sold a coat for 7 dollars, and a pair |. 
inte pantaloons for 3 dollars; how many dollars | 
| did he get for both? ee 
6. A man gave ‘ dollars for 2 harness, and 8 
dollars for a sag@le; how many dollars did he 
pay for both? ta 
7. A lady b 


| nt a 
shawl for’ 10. de 85 
| pay for both? ~~ 


t 


NE Sina pea A yee 


ADDITION. 33 


8. There are 3 red roses on one bush, 8 yellow 
roses on another, and 2 white roses on another; 
how many roses are there in all? 

9. John gave 6 apples to Mary, 5 to George, 
and kept 3 himself; how many apples had he at 
first ? g 
10. low many boys are 4 boys, 10 boys, and 7 }. 

boys? | , 

11. James has 4 rabbits in one pen, 7 in an- 
other, and 8 in a third pen; how many rabbits 
has he in all? | , 

12. Nancy had 8 yellow-birds in one cage, 5 in 

another, and 9 flying about the room; how many 

birds had she in all? 

_ 18. Lucy bought sealing-wax for § cents, paper 

for 7 cents, and a pencil for 2 cents; how many 

cents did she pay for all? 

_ 14. James bought three rose-bushes: one had 
8 buds, one 5 buds, and the other 6 buds; how 
many buds were there on all of them ? 

15. Charles had 8 cents in one pocket, 4 cents 
in another, and 5 cents in his hand; how many } 
cents had he in all? 

16. James has 8 marbles, and wins 2; then 
John gives him 4: how many marbles will he 
then have? | | 

17. Jane bought a pineushion for 6 cents, some 
icedles for 4 cents, and a pencil for 8 cents; how 
Hany cents did she pay for all ? 


CR yl ae 7 Se - St siatelapmlee 3 bc eames Mad hs cal 


a 


a 


ne UE ENN NEESER! 


LESSON I. 


Suprracrion is the operation of finding the | 
difference between two numbers. 


\ 


1. One duck gin from 2 dueks, leaves how 
many ducks? One from 2 leaves how many ¢ 


2. One duck taken from 3 3 drake, leaves how 
many ducks? One from 3 leaves how many @ 


. One duck taken from 4 Sioks. leaves how |} 
es ducks? One from 4 leaves how many ? 


4, One acorn taken from 6 acorns, ‘eaves how | 
many acorns? One from 6 leaves how many? = | 


Set a 


tea acorns? 


‘One ae 8 He o eat ss: : 


pee eee eae carter ee ene ee EE 


SUBTRACTION. 35 


1. A boy had 4 plums, and gave 1 to his sister ; 
how many had he left? Ans. 3. Why? 

Because 3 and 1 more make 4: ey la af we 

take 1 from 4, 3 will be left. 

2. Rollin found 3 ripe peaches under a tree, and 
ate 1 of them; how many had he left? 

38. A hen haded chickens, and 1 died; how 
many had she left? 

4. John has 6 acorns, and gives 1 to William ; 
how many has he left ? 

5. A tailor had 7 yards of cloth in a piece, he 
cut off 1 yard; how many yards had he left? 

6. Jane has 6 ducks, and 1 died; how many 
hwere left ? 

| 7. Julia had 10 cents, and gave 1 cent for a 
pencil; how many cents had she left? 1 from 10, 
leaves how many ! 

8. There were in a class 6 boys and 1 girl; how 
‘many more boys than girls in the class | 
_ 9. If I have § pears, and eat 1, how many are 
left? 


1 from 1 leaves 0/1 from 6 leaves 5 
1 from 2 leaves 1 | 1 from 7 leaves 6 
1 from 3 leaves 2 | 1 from 8 leaves 7 
1 from 4 leaves -3 |°1 from 9 leaves 8 
1 from 5 leaves 4 | 1 from 10 leaves 9 


Norz.—A small line is placed under what is taken away. Let the 
“obila. put its finger over what is taken away, and count what is left. 
i le ee RR RRC 
Bac ir 


te 


: 


SUBTRACTION. 


LESSON II. 


1. Two turkeys taken from 2 turkeys, leaves 
how many turkeys? 2 from 2 leaves how many? 


2. Two turkeys taken from 3 turkeys, leaves 
how many turkeys? 2 from 3 leaves how many? 


3. Two turkeys taken from 4 turkeys, leaves 
how many turkeys? 2 from 4 leaves how many? 


4, Two oranges taken from 6 oranges, leaves 
how many oranges? 2 from 6 leaves how many? 


5. Two oranges taken from 7 oranges, leaves | 
how many oranges? 2 from 7 leaves how many ? | 


car eS rll nen nr i a pnt tn mo me 


. 


a ee 


SUBTRACTION. ST 


1. Eliza picked 5 roses, and gave 2 to her 
eacher ; how many had she left? Ans. 3. anys 

Because 3 and 2 more make 5: therefore, 2 
From 5 leaves 3. 

9. Andrew had 6 chickens, and the cat caught 

2 of them;-how TARDY had he left? 

3. Aman gave 5 dollars for a hat, and 2 dollars 
for a vest; how much more did he give for the 
hat than fo the vest ¢ 

4. A farmer had 7 horses, and sold 2 of them; 
a. many had he left? 

_ A teacher asked a scholar 9 questions, mt 

he tae 2 of them; how many did he answe 
6. Jacob had 4 ge and lost 2; how1 
Shae 
AWert rode 10 inn, 5 aa walked 2 miles; 
yw many m e miles did he ride than walk? 
A drover had 8 cows, and sold 2 of them; 
OW many had he left ? 
9. Caroline had 11 books, and gave away 2; 
how many had she left ? 

10. Mary had 7 birds, and 2 died; how many 
were left? , 


2 from 2 leaves 0 | 2 from 7 leaves 5 
2 from 3 leaves 1 | 2 from 8 leaves 6 

2 from 4 leaves 2 | 2 from 9 leaves 7 
& from 5 leaves 8 | 2 from 10 leaves 8 
2 from 6 leaves 4 | 2 from 11 leaves 


, 


38 SUBTRACTION. 


LESSON III. 


1. Three hives taken from 4 hives, leaves how | 
many hives? 


9. Three hives taken from 5 hives, leaves how | 
smany_hives? 
Bi sa had 7 seen and gave 3 to Ann; how | 
_had she ear i ) 
a. “Te a. pastiii ~are-9 sheep, 3 black, and i 7 
rest are white 5 how many are white? os 
5. Sold some butter for 10 dollars, and receiv 
3 dollars; how much more is due? ale 
6. Samuel borrowed 12 cents, and paid 3; how | 
many did he then owe 2 . 
7. A merchant bought 11 barrels of flour; after | 
selling some, he Poand he had 3 barrels left; how 
many  hiirels had he sold ¢ 


3 from 8 leaves 0 | 8 from 8 leaves 5 
3 from 4 leaves 1 | 3 from 9 leaves 6 
3 from 5 leaves 2 | 3 from 10 leaves 7 
8 from 6 leaves 3 | 3 from 11 leaves 8 
3 from 7 leaves 4 | 3 from 12 leaves 9 


1. Four cars taken from 5 cars, leaves how 
nany cars ! 


2. Four cars from 6, leumes id many cars ? 


a 


chem; how many re sell? - * 7 “9: a 
A mat ‘ La 12, sola ave — DU 


nat 


6. Rufus j is 18 years old, and Betsey is 4 years 
7 ; what is the difference in their ages / 
_ 7. A lady having 5 dollars in her purse, gave 1 
follax to a beggar; how much had she left ? 
8. A boy ale fishes, and threw 4 of them 


back into the pond; how many had he left? 
: 


4 from 4 leaves 0 | 4 from 9 leaves 5 
4 from 5 leaves 1 | 4 from 10 leaves 6 
4 from 6 leaves 2 | 4 from 11 leaves 7 
4 from 7 leaves 3 | 4 from 12 leaves: 8 
4 from 8 leaves 4 | 4 from 13 leaves 9 


3. A farmer Raving 10 cows, sold all but 4 of | 


| 40 SUBTRACTION. 


| 

LESSON V. 
| oe 

| 


i Tan = 
1: Five lemons from 7 lemons, leaves how | 
many lemons ? . 


| 


2. Vive lemons from 9 lemons, leaves how | 
any lemons ? i 
_ 8. There are 6 boys and 5. girls in a class ; how | 
i -e boys than girls? Dt So | 
-| 4. Reuben ‘has 5 pi 

te John; how many has he left ? 

5. Carlos fires into a flock of 14 pigeons 
kills 5 of them; how many are left? 

6. If you eat your supper at 5 o'clock, and go} 
‘to bed at 9, how many hours have you to read } 
and play ¢ 

7. Nathan had 13 cents, and gave 5 cents for 
three pens; how many cents had he left ? | 


from 5 leaves 


5 0 | 5 from 10 leaves 5 
5’ from 6 leaves 1 | 5 from 11 leaves 6 
5 from % leaves 2 | 5 from 12 leaves 7 

| 5 from 8 leaves 3 | 5 from 13: leaves 8 | 
5 from 9 leaves 4 | 5 from 14 leaves 9 ~ 


eer aa nin pion = A 


i Se 


SUBTRACTION. 41 


~ 


1. Six oranges from. i oranges, leaves how 


lany oranges ¢ é 


iy or Taos — 
3. A bo i 8 cents for a top, and so 
‘cents ny many cents did he lose? = 
her; how many did he keep for himself? 
| al there are 16 boys and 6 girls; _ 
ow many more boys than girls are there? 
6. There are 14 sheep in a fold, and a wolf kills 
of them; how many are left alive? | 
7. A grocer bought 8 cheeses; after selling 
me, he found he had 6 left: how many were 


from 11 leaves 


from 6 leaves 
7 from 12 leaves 


leaves 


8 leaves 
from. 9 leaves 
0 leaves 


from 14 leaves 
from 15 leaves 


m= WOOD Fr © . 


a 


aa 


49, SUBTRACTION. — 
ee ee se re ee 


2. Seven cherries from nine cherries, leaves 
row many cherries ? , 


3 


Theres»were 7 chairs in a room, and Mary 


| took Tout; au a, any doh ; 
| 4, There were 10 doveson the roof of the barn 


| and 7 flew away; how many were left ? 
| 5. Frank having 15 cents, spent 7 eents fd 
toys; how many cents had he left? 7: 
6. A farmer having 16 pigs, sold them all but 

6; how many did he sell? 

| 7. Julia, finding 14 roses in bloom, picked them 


» 


all but 7; how many did she pick ? | 
8. Twelve cents, less 11 cents, are how many ¢ 


7 from 7 leaves 0! 7 from 12 leaves 5% 
7 from 8 leaves 1 | 7 from 13 leaves 6 
7 from 9 leaves 2 |-7 from 14 leaves 7 
7 from 10 leaves 3 | 7 from 15 leaves 8° 
7 from 11 leaves 4 | 7 from 16 leaves 9. 


ah ; 


eee 


SUBTRACTION. 43 


————$—_—___— —— 


LESSON VIII. 


bbbbddde 


i. Eight bottles from 8 bottles, leaves how 
many bottles ¢ 


bhddbddada 


2. Eight bottles from nine bottles, leaves how 
many bottles? 

3. Mr. Jones bought 12 firkins of butter, and 
sold 8 of them; how many had he left? 

4. James is 11 years old, and John 10 years 

ld; what is the difference of their ages? 

5. A boy carried 9 quarts of berries to market, 
and sold 8 quarts; how many had he left? 

6. From a class of 17 boys, 8 are taken and put 
into a higher class; how many are left? 

7. There are 14 shade-trees in arow; 8 of them 
die: how many are left? | 

8. Ten dollars less 8 dollars, are how many ? 


8 from 8 leaves 0 | 8 from 18 leaves 5 
8 from 9 leaves 1 | 8 from 14 leaves 6 
8 from 10 leaves 2 | 8 from 15 leaves 7 
8 from 11 leaves 3 | 8 from 16 leaves 8 
& 4 | 8 from 17 leaves 9 


from 12 leaves 


La 


| 44 SUBTRACTION. 


a na an i 


LESSON IX. 
(868886 8008680 


1. Nine balls taken from twelve balls, leaves 
how many balls? 


@@ 8&6 06686 8860 


2. Nine balls from 13 balls, leaves how many? 

3. A lady having 15 dollars, gave 9 dollars for 
a bonnet; how many dollars had she left? - 

4. Harriet has a writing-book of 12 pages; she | 
has written 9 pages: how many pages are left? 

5. The school-term is 14 weeks long; 9 weeks 
have passed: how many weeks remain ? 

6. A boy had 18 peaches, and sold 9 of them ; 
Sh many had he left? 

. Ina certain school, there are 17 boys and 9 | 

| paw how many more boys than girls? 

8. In an orchard are 13 pear-trees, and 9 of 
them die; how many are still alive? 

9. Ghavles bought a knife for 11 cents, and gold | 

it for 9 cents; how many cents did he lose? 


9 from 9 leaves 0 | 9 from 14 leaves 5 
9 from 10 leaves 1 | 9 from 15 leaves 6 
9 from 11 leaves'2 | 9 from 16 leaves 7 | 
9 from 12 leaves 3 | 9 from 17 leaves 8 | 
9 from 13 leaves 4 | 9 from 18 leaves 9 


i 


SUBTRACTION. 45 


LESSON X. 
0260000000606 80 


1. Ten balls from 14 balls, leaves how many 
balls 


@86 80008608 8 6 4 0086 


2. Ten balls from fifteen balls, leaves how 
many balls? 

8. Horace put 14 dollars in the savings bank, 
and drew out 10 dollars; how many dollars were 
left in ? 

4. A boy earned 18 cents, and received 10 cents; 
how much was still due him / 

5. William shot 16 pigeons, and gave 10 away ; 
how many were left ? 

6. Mary had 19 pins, and lost them all but 10; 
how many did she lose? 

7. Harry borrowed 11 cents, and paid 10 cents; 
how many cents did he still owe? 

8. Edgar had 12 marbles, and lost 10; how | 
many had he left? 


10 from 10 leaves 0 | 10 from 15 leaves 5 
10 from 11 leaves 1 | 10 from 16 leaves 6 
10-from 12 leaves 2 | 10 from 17 leaves 7 
10 from 13 leaves 3 | 10 from 18 leaves 8 
10 from 14 leaves 4 | 10 from 19 leaves 9 


a ne OS, 


46 


SUBTRACTION. 


LESSON XI. 


REVIEW LESSON. : 
6 from 11, how many? | 8 from 10, how many? 
5 from 10, “ 6 from 12, 3: | 
4 from 8, ie 9 from 11, “ 
9 from 12, x 8 from 13, % 
7 from 12, ms 3 from 8, . 
6 from 7, f 7 from 10, ‘ 
9 from 10, Ms 5 from 11, 
5 from 9, us 8 from 15, re 
2 from 8, . 4 from 7, ti 
2 from 10, how many? | 4 from 12, how many? 
7 from 9, $6 § frome. a 
Setrom alo | 96 6 from 13, s 
9 from 14, 4 from .< (85 
5 from’ 8, 9 from 16, . 
3 from 7, S 8 from 12, 1" 
2 from 11, T from 13, i 
Gafrom’” 9, ca 5 from 12, s 
7 from 16, Hf 3 from 10, aS! 
8 from 14, how many? | 4 from 13, how many? 
9 from 17, * 6 from 10, A 
5 from 18, 8 from 11, “ 
3 from 11, ‘g 9 from 18, % 
7 from 14, * 6 from 15, if 
2 from 9, 2 3 from 12, 
4 from 10, v¢ 4 from 9, ae 
8 from 17, rf 7 from 11, ni | 
7 trom 15, $e 9. fron 15,” wai es 


SUBTRACTION. 47 


LESSON XII. 


PROMISCUOUS EXAMPLES. 


1; Ifenry had 18 cents; he gave 4 cents for an 
orange, and 6 cents for a pencil; how many cents 
had he left ? 

Awnatysis.—He had left the difference between’ 
(18 cents and the sum of & cents and 6 cents: the 
sum of 4 and 6 is 10: Therefore, he had left 18 

cents less 10 cents, which vs 8 cents. 


Ce eS Se ee 


2. A boy gave 20 cents for a sled, and 5 cents 
to have it painted; he then sold it for 15 cents: 
‘how many cents did he lose? 
3. A farmer bought a sleigh for 19 dollars, and 
paid a ten dollar bill, and a five dollar bill; how 
much did he still owe? 

4. A drover bought 4 pigs of one man, and 8 
of another; he sold five: how many had he left ? 
5. Eli’s father gave him 15 cents on Christmas; 
he bought a book for 7 cents, and gave 6 cents to 
a beggar; how many cents had he left? 

6. John earned 10 cents, and found 6 cents; he 
then bought a slate for 9 cents; how many cents 
had he left? | 

7. A farmer had 9 sheep in one lot, and 9 in 
another; he sold 7 of them: how many were left / 
8. There were 18 scholars in a school, of which 
9 were boys; how many girls were there? 


. e 5 yy ay 
oe wr ( 


LE S'S ONST. 


MULTIPEICATION. 


Mouttiprication is the operation of taking one 
number as many times as there are units in | 


another. 


1. One orange, taken once, is one orange. 


5. Five oranges, taken once, is 5 oranges. 


once 
once 
once 
~ ONCE 
once 


Orv He Oo bD me 


18 
is 
is 
is 
is 


once 
once 
Once 
once 
once 


SCO Ot SD 


MULTIPLICATION. 49 


LESSON II. 


1. James has 1 apple in each hand; how many 
has he in both hands? 


Two times one, are how many ? 
2. Charles has two apples in each hand; how 
many has he in both hands? 


Two times two, are how many ? 


3. John has 3 apples in one basket, and 3 in 
another; how many apples in both baskets? 


Two times three, are how many ¢ 


4. Here are four pears in one row, and 4 in 
another; how many pears in both rows? 


Two times four, are how many 


5. Here are five cherries in one row, and 5 in 
another; how many cherries in both rows? 


Two times five, are how many ¢ 


3 


Fn 


: 
{ 
| 
| 


50 


MULTIPLICATION. 


6. Here are six bottles in one row, and 6 in | 
another; how many bottles in both rows? 


bddbdd 


Two times six, are how many ? 


7. Here are seven soldiers in one row, and seven 
how many soldiers in both rows? 


adda do 


in another ; 


“RAAB ARE 


Two times seven, are how many ? 


8. John has two piles of apples, and 8 apples in 
how many apples has he? 
9. Charles has 2 piles of apples, and 9 apples 
in each pile; how many apples has Charles? 
10. James has 2 piles of apples, and 10 apples 
| in each pile; how many apples has James? 
11. Lucey has 6 roses on one bush, and 6 roses 


each pile ; 


‘on another; how many roses has she? 


12. James has 5 birds in one cage, and 5 in 


another cage; how many birds has he? 


13. Nancy shes two pieces of tape, each 4 yards 


long; how many yards of tape has she? 


_times 
times 
times 
times 
times 


ee 


1 


bs) 


ou pe 


are 
are 
are 
are 
are 


pomsy 
=) 


CO o> He bo 


bo bo bo bo 


bo 


times 6 are 
times 7 are 
times 8 are 


times 9 are > 


times 10 are 


TTT) 


ty 


20 


ee Or ee ee enna! 


MULTIPLICATION. 51 


LESSON III. 


1. Here are 3 turkeys. Now, if each turkey 
costs 4 shillings, what will the 3 turkeys cost ? 


Awnatrysis.—TZhree turkeys will cost 3 times as 
much as 1 turkey: 1 turkey costs 4 shillings: 
Therefore, 3 turkeys will cost 3 times 4 shillings, 
which are 12 shellings. | 


2. What will 8 axes cost, at 2 dollars apiece? 
. If one sheep costs 3 dollars, what will be the 

sk of 3 sheep ¢ 

4. Joseph gave 3 apples apiece to 3 of his com- 
panions; how many apples did he give to all? 

5. If a farmer gives 7 bushels of corn for one 
yard of cloth, how much must he give for 3 yards ¢ 

6. If Sarah reads 9 pages a day, how many 
pages will she read in 3 days? 

7. What will be the cost of 5 yards of ribbon, 
at 3 shillings a yard? 


a 


times 6 are 18 


8 times 1 are 8} 3 

8 times 2 are 6 | 38. times are 21 
3 times 3 are 9 8 times S$. are 24 
8. times 4 are 12 | 8 times 9 are 27 
3 times 5 are 15 | 3 times 10 are 30 


59 MULTIPLICATION. 


LESSON IV. 


1. Here are 4 hives: If 1 hive costs 3 dollars, 
what will 4 hives cost? 


2. If John rides 7 miles an hour, how far will 
he ride in 4 hours ? 

8. A drover bought 6 calves, at 4 dollars apiece; 
how much did he pay for them ? 

4, If there are 9 gallons of cider in 1 keg, how 
many gallons would there be in 4 kegs? 

5. If there are 4 weeks in one ‘month, how 
many weeks are there in 4 months? 

6. If there are 9 panes of glass in one window, 
how many panes of glass are faced in 4 windows ? 

7. At 10 shillings a day, what will 4 days’ 
work come to? 

8. If 4 boys have 8 marbles apiece, how many 
will they all have? 
_. 9. What will 9 hats cost, at 4 dollars apiece? 


4 times 1 are 4{|4 times 6 are 24 
4 times 2 are 8} 4 times 7 are 28 
4 times’ 3 are’ 12 |} 4. times 8 - are 32 
4 times 4 are 16 | 4 times 9 are 8 

4 times 5 are 20 |4 times 10 are 40 


MULTIPLICATION. 53 


LESSON V. 


1. If 1 car has 4 wheels, how many wheels 
have 5 cars? 


2. What will 5 quarts of berries cost, at 8 cents 
a quart ? 

3: If there are 7 trees in a row, how many trees 
are there in 5 rows? 

4. What will 5 yards of ribbon cost, at 6 cents 
a yard ? 

5. If a boat sails 3 miles an hour, how far will 
it sail in 5 hours? 

6. George bought 5 books, at 10 cents apiece; 
what did they all cost him? 

7. What will 5 pounds of sugar cost, at 9 cents 
a pound ? 

8. If a boy goes to school 5 days in a week, 
how many days would he go to school in 5 weeks? 

9. What will 5 melons cost, at 10 cents apiece? 


iB} times 1 are 571 5 times “6. .are,730 
5 times 2 ‘are 10'| 5 times -7 are 85 
5 times 38 are 15.| 5 times 8. are 40 
5 times 4 are 20! 5 times 9 are 45 
5 5 are 25 | 5 times 10° are 50 


times 


Sap SV: REE PERERRRAARRIRDN | 


54 MULTLILPLPROATION. 


LESSON VI. 


1. Here are 6 sheep: A farmer paid 3 dollars 
for each sheep; how much did he pay for the 
6 sheep ¢ 


2. If aman eats 8 ounces of meat in a day, how 
many ounces would he eat in 6 days? 

3. In an orchard are 6 rows of trees, and 10 
trees in a row; how many trees in the orchard ? 

4. If-an apple is worth 4 cherries, how many 
cherries are 6 apples worth ? 

5. Charles gave 6 beggars 6 cents apiece; how | 
many cents did he give to them all? 

6. What will be the cost of 6 watches, at 9 
dollars apiece ? 

7. If a scholar works 7 examples in one hour, 
show many can he work in 6 hours ? 

8. If 1 pencil costs 2 cents, what will be the 
cost of 9 pencils ? 


6 times 1 are 6 | 6 times 6 are 36 
6 times 2 are 12 | 6 times 7 are 42 
6 times 3 are 18 | 6 times 8 are 48 
6 times 4 are 24 | 6 times 9 are 54 
6 times 5 are 30: 6 times 10 are 60 


MULTIPLICATION. 


LESSON VII. 


1. Here are 7 bells: If 1 bell costs 2 dollars, 4 
what will be the cost of 7 bells? 


. If 1 hat costs 4 dollars, what will be the cost: 
of 7 7 sabi 
3. What will 7 pounds of rice cost, at 5 cents a [> 
| pound ¢ 7 
4, James has 7 brothers, and gives to each 9 
marbles; how many does he give to them: all ? 
5. William gives 7 apples to each of 9 school- 
mates; how many apples does he give away ? 
| 6, At 10 cents apiece, what will be the cost of 
| 7 pineapples / 
' 


7. How much will 7 yards of calico cost, at 9 
a a yard / 
. What will 7 tops cost, at 9 cents for each | 
ve 
9. At 5 cents each, what will 7 tops cost ? 


| 7 times 1 are 7|7 times 6 are 42 

| 7 times 2 are 14 | 7 times 7 are 49 

| J times 3 are 21 !|7 times 8 are 56 
7 times 4 are 28 | 7 times 9 are 63 
7 times 5 are 35 | 7 times 10 are 70 


56 MULTIPLIOATION. 


LESSON VIII. 


1. Here are 8 mugs: If 1 mug costs 3 shillings, 
} what will be the cost ef 8 mugs? 


. What is the cost of 8 pounds of rice, at 5 
al a pound ¢ : 

. 8. If a horse travels 7 miles in an hour, how far | 
will he travei in 8 hours? 

4, At 9 cents a dozen, what will 8 dozen of 
egos cost ? 

» 5. William bought 8 pens, at 2 cents apiece; | 
what did the pens cost ? | 
_ 6. If William sells 8 quarts of cherries, at 4 
cents a quart, how much will they come to? 

‘ 7. If a man earns 9 dollars in one month, how 
ae will he earn in 8 months? 

_ If 1 plate costs 10 cents, what will 8 plete | 

ae : a 

9. At 3 cents each, what will 8 wih gaa cost ! 


8 times 1 ‘are 8 /| 8 times 6 are 48 

8 times 2 are 16) 8 times 7 are 56 

8 times 3 are 24 | 8 times 8 are 64 
8 times 4 are 32 | 8 times 9 are 72 ~ 
8 times 5 are 40; 8 times 10 are 80 


ee 


MULTIPLICATION. 57 


- at the same rate? 


LESSON IX. 


1. If 1 pear costs 2 


cents, what will 9 pears cost, 


_ 2. If one cord of wood costs 3 dollars, what 
_ will 9 cords cost ¢ 


a pound ? 


8. What will 9 pounds, of lard cost, at 7 cents 


4, If one week’s board costs me 5 dollars, what 
will 9 weeks’ board cost me? 


5. If a family consumes 8 pounds of butter in a 
week, how many pounds will they consume in 9 


} 
i 
! weeks ¢ 


6. At 9 


ee 
aa cost ¢ 


cents a pound, what will 9 pounds of 


. What will be the cost of 9 sheep, at 2 dol- 
. bia apiece ¢ c 
8. If Jane writes 6 lines a day, how many lines 
: will slye write in 9 days? 


| 0 times 
. 9 times 
| 9 times 
_ 9 times 

9 times 


are 
are 
are 


9 
18 
27 
56 
45 


9 times 6 are 54 
9 times 7 are 63 
9 times 8 are 72 
9 times 9 are 8l 
9 


times 10 are 90 | 


3% 


Sa TS PP TP Ome LONs 


1 or 
Obhe. 


LESSON X. 


1. If 1 chair costs 2 dollars, what will 10 chairs 
cost, at the same rate ¢ 


FoR Pah Ph ah 


aa 
| 
. If James gave 4 apples for one orange, how 
ay apples must he give for 10 oranges ? 
3. At 6 cents a quart, what will 10 quarts of 
strawberries cost ? 
4. If a man travels by stage, at the rate of 3 
miles an hour, how far will he travel in 10 hours? 
5. There are 4 quarts in one gallon, how many 
quarts are there in 10 gallons ? 
6. What will 10 paras of broadcloth cost, at 5 
pal ayard?  — 
. If a barrel of potatoes costs 7 shillings, how | 
meh will 10 barrels cost? — 
. Ten cents make one dime; how many cents 
are hes: in 10 dimes? 
9. At 4 cents each, what will 10 ats qgst? 2 
gsacemeeiea la epi d Sous Mia aa 


10 times 
10 times 
10 times 
10 times 
1@ times 


are 10 | 10 times 6 are 60 
are 20 10 times 7 are 70 
are 30 | 10 times 8 are 80 
are 40 10 times 9 are 90 
0 


are 100 


Sou HR £9 bo He 


are 50 | 10 times 1 


MULTIPLICATION. 59 


LESSON XI. 


REVIEW LESSON. 


me 
— . 
ond 
© 
is 9 

‘ 
or 


2 times 9 are how many?/8 times 3 are how many? 
Tt “ 6 times 4: ve | 
5 times 9 a 9 times 5 7 | 
8 times 4 se 5 times 8 cl 

| 4 times 9 2 times 8 i." 

| 6 times 3 a 5 times 7 “ 

| 9 times 4 ; 9 times 3 + 

| 7 times 5 Be 4 times 7 o 
3 times 9 7 '6 times 5 <s 


8 times 8 arehow many?|9 times 8 are how many? | 


4 times 6 tn '4 times 4 as 
3 times 8 as 8 times 5 ae 
9 times 7 se 2 times 6 ht 
6 times 6 6 times 9 
| 7 times 3 & 4 times 3 a3 
5 times 6 ite 9 times 9 id 
6 times 8 “ 4 times 2 - 
8 times 9 “d 7 times 7 iy 


7 times 4 are how many ?|6 times 2 are how many? | 


3 times 6 * 3 times 6 i 
5 times 3 ie 7 times 9 i 
% times 8 ee 2 times 3 “6 
8 times 6 My 3 times 3 a 
| 2 times 5 “ ‘9 times 8 « 
3 times 4 sé LB times 9 a 
3 times 5 ba 2 times 4 s 


5 times 4 $6 0 times 9 ¢ | 


60 MULTIPLICATION. 


LESSON XII. 


1. If 1 yard of cloth costs 4 dollars, what will 7 
yards cost ? 
2. There are 7 days in a week; hoe many days 
are there in 4 weeks? In 5? if} 7? In8? In9? 
3. If 1 apple-tree bears 9 bushels of apples, how 
many bushels will come from 6 trees? 57 9% 7? 
4. Ifa cannon-ball weighs 10 pounds, how many 
pounds will 8 balls weigh? 9% 6%-5% 4? 
5, Albert had 5 times as many marbles as James, 
and James had 7; how many had Albert? 
6. A farmer had 3 yards, with 9 sheep in each ; 
how many sheep had he in all? 
7. If a man earns 10 dollars a month, how much 
vill he earn in 5 months? Ini month? In 7? _ 
8. How much are 6 times 7 7 PE 6% 5 times 9, 
plus 5? 8 times 4, plus 3? 7 times 1, plus 9? 
9. How many are 4 times 5 less 6? 5 times 8, 
less 4% 7 times 3, less 5? 9 times 2, less 10? 
| How many are 6 times 7, plus 9? 
| 10. James sold a chicken for 18 cents, his top 
_for 8 cents, and his marbles for 12° cents; what 
| did he get for them all ? 
| 11. Lucy bought 7 yards of tape at 5 cents a 
| yard, and 2 yards of ribbon at 3 cents a yard; 
| what did she pay in all? 


PROMISCUOUS EXAMPLES. 


MULTIPLICATION. 61 


12. If a cow is worth 26 dollars, what are 2 
cows worth ? 


| Awnatysis.— Two cows are worth twice as much 

| as 1 cow: 1 cow ts worth 26 dollars: Therefore, . 
cows are worth twice 26 dollars. Twice 2 tens are 
40, and twice 6 units are 12 units: 40 and 12 are 
52: Therefore, if 1 cow is worth 26 dollars, 2 
cows will be worth 52 dollars. 

13. If it costs 24 cents a week to keep a cow, 
how much will it cost to keep 4 cows? 

14. If the cars go 16 miles an hour, how far 
will they go in 6 hours ? 

15. At 45 cents a bushel for oats, what will 2 
bushels cost? 

16. If a man earns 18 dollars in one month, ' 
how much will he earn in 5 months? 

17. At 14 cents a pound, what will 7 pounds of 
butter cost ¢ i 

18. At 28 cents a bushel, what will 3 bushels | 
of apples cost? —- 

19. Joseph is 19 years old, and the age of his | 
father is 4 times as great; how old is his father? | 

90. An orchard contained 17 peach-trees, and 5 
times as many apple-trees; how many apple-trees 
were there? 

91. A tailor bought 5 pieces of cloth, each piece 
containing 15 yards; how many yards did he buy 
in all? | 


DIVISION. 


LESSON I. 


1. When a number is divided into 2 equal 
parts, each of the parts is called, one-half. 


| Here are 2 apples: What is the half of 2 apples? 
What is the half of 2? 


Here are 4 apples: If they be equally divided 
between 2 boys, how many apples will each boy 
| have? 
Awatysis.—The half of a number taken 2 times 
ds equal to the number: 2 taken two times is 4: | 
| Therefore, 2s the half of 4, and each boy will | 
| have two apples. 


What is one-half of 6 apples? One-half of 6? 


. : 2. When a number is divided into 3 equal | 
| parts, each of the parts is called, one-third. 


Here are 3 lemons:. What is one-third of 3 
lemons? What is one-third of 3? 


Somer es 


eee “ a 


DIVISION. bi 


evs are six eee What is one-third of six 
lemons? What is one-third of 67 


3. When a number is divided into 4 equal 
parts, each of the parts is called, one-fourth. 


. Here are 4 ducks: What is one-fourth of 4 
ducks? What is one-fourth of 4? 


| 
| 
/ 
/ 
| 
: 
| 
: 
| 
| 
| 
| 
| 


Here are 8 oranges: What is one-fourth of 8 
oranges? What is one-fourth of 8? 


4, When’ a number is divided into 5 equal 
parts, each of the parts is called, onezifth. 


Here are 5 watches: What is one-fifth of 5 
| watches? What is one-fifth of 5% | 


| Here are 10 trees: What is one-fifth of 10 
'trees? What is one-fifth of 10? 
> Seer 


7 
| 


64 DIVISION. 


{ 
5. When a number is divided into 6 equal | 
parts, each of the parts is called, one-sewth. | 


Here are six axes: What is one-sixth of 6 axes? 
What is one-sixth of 6? 


Here are 12 axes: What is one-sixth of 12 
axes? What is one-sixth of 12? 


6. When a number is divided into 7 equal 
parts, each of the parts is called, one-seventh. 


Here are 7 acorns: What is one-seventh of 7 
acorns? What is one-seventh of 7 ? 

What is one-seventh of 14 oranges? What is 
one-seventh of 14? 


7. When a number is divided into 8 eqital | 
parts, each of the parts is called, one-eeghth. 


AKAD AAI 


Here are 8 boots: What is one-eighth of 8 
boots? What is one-eighth of 8? 


DIVISION. 65 


What is one-eighth of 16 boots? What is one- | 
eighth of 16% 

8. When a number is divided into 9 equal 
parts, each of the parts is called, one-ninth. 


@@228288288 


Here are 9 trees: What is one-ninth of 9 trees ! 
What is one-ninth of 9? | 

What is one-ninth of 18 trees? What is one 
ninth of 18 ? 


9. When a number is divided into 10 equal 
parts, each of the parts is called, one-tenth. 


Here are 10 hats: What is one-tenth of 10 
hats? What is one-tenth of 10? 
What is one-tenth of 20 hats? One-tenth of 20% 


10. How do you find one-half of a number? 
Ans. By dividing the number by 2. 

What is one-half of 22 Of 4? Of 10? 

11. How do you find one-third of a number? 
Ans. By dividing the number by 3. 

What is one-third of 8%. Of 6? Of 12? 


12. How do you find one-fourth of a number 4 
Ans. By dividing the number by 4. 
What is one-fourth of 44 Of 8? Of 12% 


Put similar questions to include the one-tenth. 


‘ 


66 DIVISION. 


LESSON II. 


Drvision is the operation of finding how many 
times one number is contained in another. 


1. Which is the greater, 1 apple or 2 apples? 
2 apples are how many times as great as | apple? 


is contained in 2 apples, 
1 in 2, how many times? 


2. 2 apples are contained in 2 apples, 
how many times? 2 in 2, how many times? 


)) 
eal L, 


8. 2 apples are contained in 4 apples, 
how many times? 2 in 4, how many times? 


how many times? 2 in 6, how many times? 


5. 2 cherries are contained in 8 cherries, | 


4. 2 pears are contained in 6 pears, 
| 
how many times? 2 in 8, how many times? | 


ie 
| 
c 
| 


DIVISION. 67 


Se 


. Four apples are how many times as great 
as 2 apples? 


Awatysis.—Lour apples are as many times as 
great as 2 apples, as 278 contained times in 43 2 
is contained in 4,2 times: Therefore, 4 apples are 
2 times as great as 2 apples. 


7. How many times are 8 pears as great as 2 
pears? 2 in 8, how many times? bs 

S. How many times are 12 marbles as great 
as 8 marbles? 38 in 12, how many times? 

9. par aa sticks of candy are how many times 
as great as 2 sticks of candy? 2 in 18? 

10. Sixteen are how many times 2? 2 in 16, 
how many times? 

11. Ten are how many times 57 5 in 10} how 
many times ? 

12. Fourteen are how many times 7? 7 in 14, 
how many times / | 

13. Twelve are how many times 2? 2 in 12, 
how many times ¢ 

14. Two apples are contained how many times 
in 16 apples? 2 in 16, how many times ? 


Satin. 2, once. | 2 in 12, 6. times. 
2 in 4, 2 times. | 2 in 14, 7 times. 
2 in 6, 38 times. | 2 in 16, 8 times. 
2 in 8, 4 times. 2 in 18, 9 times. 
2? in 10, 5 times. | 2 in 20, 10. times. 


Se EE 


6s DIVISION. 


t 
i 


| LESSON III. 


/ 
1. John divided 9 acorns, equally, among his 
_ three brothers; how many did he give to each ? 


Awatysis.—l7e gavg to each brother one-third 
of 9 acorns: one-third of 9 is 8: Therefore, he 
gave each brother, 3 acorns. 


, 2. Twelve scholars, in a school, are distributed | 
_ equally on 3 benches; how many sit on cach bench? 
38. James buys 15 oranges, and divides them 
equally among 3 boys; how many has each boy ? 
_ 4, William divided 21 plums, equally, among 3 
_of his companions; how many did he give to each ? 
_ 5. A farmer put 30 sheep into 3 pens; how 
| many did he put in each pen? 
' 6 Charles earned 27 cents in 3 days; how 
_many cents did he earn each day ? 
7. If 24 marbles are divided, equally, among 3 
boys, how many will each boy have? 


Paine. 8, once. | 38 in 18, 6. times. 
Pore se OD temer 8 in woh, timesn: 
| dein 9, 8 times. | 3 in 24,. 8 times. 
| 8 in 12,. 4 times. | 3 in 27, 9 times. 
| 3 aie 16.) 5) times 1/3. in #30; 10) times, 


DIVISION. 69 


LESSON IV. 


1. If 4 barrels of apples cost 12 dollars, how 
mapy dollars will 1 barrel cost ? 
Anatysis.—One barrel of apples will cost one- 
| fourth as much as 4 barrels: 4 barrels vost 12 
dollars, one-fourth of which ts 3 dollars: There- 
| Sore, 1 barrel of apples will cost 3 dollars. 


2. If 4 yards of cloth cost 8 dollars, what will 
1 yard cost ? 
3. If 4 oranges cost 20 cents, how much will 1 
| or ange cost ? 
4, Te 4 pineapples cost 36 cents, how much is 
that apiece ? 
5. If 40 dollars will buy 4 coats, how much 
does each coat cost ? 
| 6. If 28 cents will buy 4 melons, what is the 
_ cost of 1 melon ? 
| 7. If James pays 32 cents for 4 tops, how much 
| does each top cost him? — 
_ 8. Jane paid 36 cénts for 4 yards of ribbon; 
how much did she pay for 1 yard # 


fa ES), ae once. | 4 in 24, 6 times. 
| 4 in 8, 2 times. | 4 in 28, 7° times. 
| 4 in 12, 8 times. | 4 in 82, 8 times. 
| 4 in 16, 4 times. 4 in. 36, 9 times. 
| 4 in 20, 5 times. ! 4 in 40, 10 times 


70 DIVISION. 


LESSON V. 


1. If 20 dollars will buy 5 yards of broadcloth, 
how much is that a yard ? 


2, At 5 dollars a week, how many weeks’ board | 


pee I obtain for 35 dollars ? 
. If 5 men pay a bill of 15 dollars, how much 
ae each man pay ? 


4. If 5 scholars can sit on 1 bench, how many | 


benches will accommodate 50 scholars ? 

5. How many barrels of flour can be bought 
for 40 dollars, at 5 dollars a barrel ? 

6. low many hours will it take a man to travel 
10 miles, if he travels 5 miles an hour? 


A man paid 45 dollars for building 5 rods of | 


fence; how much did he pay for 1 rod? 

8. If I put 25 bushels of apples into 5 boxes, 
how many do I put in each box? 

9. A person received 50 dollars for 5 weeks’ 
labor; how many dollars did he receive in one 
week ? | 

10. If | receive 5 dollars for 5 bushels of wheat, 
how much is that a bushel? 


Rican B, once. atnaciulte) aut By an ces?) “Gey time 
Pain 10, -2.times: | 5. inic3h, ‘7. times, 
5 in 15, 38 times. te 5 in 40, 8 times. 
jean .20, 4 times. | 5 in 45, 9. times. 
5” in 25, 5 times. 7 5 ma) 50, - 10% times, 


DIVISION. 711 


LESSON VI. 


1. If 6 sheets of paper make a copy-book, how | 
many books will 18 sheets make? 
2. If 24 peaches be equally divided among 6 | 
boys, how many will each have? ‘ 
3. At 6 cents a yard, how many yards of ribbon | 
can te bought for 42 cents? : 
. At 6 shillings 2 day, how many days’ board | 
can is obtained for 36 shillings ? 
5. A butcher paid 30 dollars for 6 calves; how | 
much did he pay apiece 4 
6. If Mary reads 6 pages a day, how many days 
will it take her to read 48 pages % 
7. [fa ship sails 6 miles an hour, how long will | 
it take her to sail 54 miles # 
8. I gave 12 dollars for 6 bushels of wheat; 
bin did I pay a bushel? 
| . A mason finds that he can build 60 rods of 
Bris fence in 6 days; how many rods can he 
build in one day ? 
10. If 6 men can build 6 rods of wall in one 
day, how much can one man so age dessa 


OH. « JG) once. | 6 Be vom, Be 36, 6 times. 
6 in 12, 2 times. | 6 in 42, 7 times. 
6 in 18, 3 times. |.6 in 48, 8. times. 
| 6 in 24, 4 times. | 6 in 54, 9 times. 
6 in 30, 5 times. | 6 in 60, 10 times. 


2 DIVISION. 


LESSON VII. 


1. How many pounds of sugar, at 7 cents a 
‘pound, can be bought for 28 cents ? 

2. Susan gave 21 cents for 7 pencils; how : 
/many cents did she give for one pencil? 

3. A boy sold 7 baskets of strawberries for 56 
cents; how much did he get a basket? 

4, A farmer received 14 dollars for 7 pigs; 
what did he receive for 1 pig? 

5. A farmer has 35 dollars, which he wishes to 
expend in plows; he finds that they are 7 dollars | 
apiece: how many can he buy? 

6. If a stage runs 49 miles in 7 hours, how far 
does it run in one hour? 

7. If 7 dozen of eggs are worth 63 cents, what 
is one dozen worth ? 

8. There are 7 days in one week; how many 
weeks are there in 56 days? 

9. I paid 70 cents for 7 yards of calico; how 
much did I pay for one yard ? 

10. George bought 7 apples, for which he gave 
7 cents ; eae bith did he give apiece? 


Fran 8, once. | 7 in 42, 6 times. 
7 in 14, 2 times. | 7 in 49, 7 times. 
fan? 21, Be times: | Fane o6, 8s dimes: 
7 in 28, 4 times. | 7 in 638, 9 times. 
7 in’ 35, 5 times. | 7 in 70, 10 times. 


DIVISION (3 


LESS ONGV EIT. 


tl. A lady purchased 8 yards of ribbon for 48 
cents; what did one yard cost? 

2. A gentleman bought 8 yards of broadcloth 
for 32 dollars; what was the cost of one yard? 

3. At 8 cents a pound, how many pounds of 
ginger can be bought for 40 cents? 

4. I paid 16 dollars for 8 barrels of apples; 
what did I pay for one barrel ? 

5. There are 8 quarts in one peck; how many 
pecks are there in 24 quarts? 

6. When 80 dollars are paid for 8 acres of land, 
what is paid for one acre? 

7. At 8 dollars a month, how long must a per- 
son work to earn 64 dollars? 

8. If one tree bears 8 bushels of apples, how 
many trees will yield 56 bushels? 

9. Josevh so!d 8 melons for 72 cents; what was 
the price of one melon? 

10. if a tailor requires 8 yards of cloth to make 
1 suit of clothes, how many suits of clothes will 
32 yards of cloth make? 


8 in 8, once. | 8 in 48, 6 times. 
8 in 16, 2 times. | 8 in 56, 7 times. 
8 in 24, 8 times. | 8 in 64, 8 times. 
8 in 32, 4 times. | 8 in 72, 9 times. 
8 in 40, 5 times. | 8 in 80, 10 times. 


74 DIVISION. 


LESSON IX. 


1. At 9 cents apiece, how many melons can be 
bought for 27 cents? | 

2. How many yards of calico, at 9 cents a yard, 
can be bought for 54 cents? 

3. If a horse eats 9. bushels of oats in a month, 
how long will 36 bushels last him ? 

4. If a horse travels 9 miles an hour, in what 
time will he travel 90 miles? 

5. If 9 sewing girls received 45 shillings for a 
day’s work, how much did each receive? — 

6. In an orchard there are 81 trees, and 9 trees 
in a row; how many rows in the orchard ? 

7%. A farmer divided 18 bushels of potatoes, 
equally, among 9 persons; how many bushels to 
each person ? 

8. How many yards of silk, at 9 shillings a 
yard, can be bought for 63 shillings? 

9. A workman received 9 dollars fer 9 days’ 
work; what were his daily wages ? 

10. If a man spends 9 cents a day for cigars, 
how long will 72 cents last him? 


On <9, once. | 9 in 54, 6 times. 
9 in 18, 2 times. | 9 in 68, ‘7 times. 
9 in 27, 3 times. |.9-m 72, 8 times. 
9 in 36, 4 times. | 9 in 81, 9 times. 
9 in 45, 5 times. | 9 in 90, 10 times. 


DIVIBION. 


LESSON X. 


1. At 10 cents a quart, how many quarts of 
molasses can be bought for 50 cents? 


2. At 10 cents apiece, how many melons can be 
bought for 70 cents ? 
3. A farmer had 40 sheep, and put 10 in a 
flock; how many flocks had he? 
4, Thats are 10 cents in one dime; how many 
dimes are there in 80 cents ? 
5. How many calves will 60 dollars buy, at 10 | 

| 

| 


dollars each ? 


6. At 10 cents a yard, how many yards of 


| calico can be bought for 90 cents ¢ Y 


7. Paid 20 dollars for 2 colts; what was the | 
bo of one colt ¢ | 
. If a boy earns 10 cents a day, how long will 


it say him to earn 70 cents? 


9. A grocer finds that he can buy cider for 10 
dollars 2 barrel; how many barrels of cider can 
he buy for 30 dollars 2 

10. How many pineapples, at 10 cents apiece, 


ean I buy for 100 cents? 


10 
10 
10 
10 
10 


10, 
20, 
30, 
40, 
50, 


10 
10 
10 
10 
10 


in 


60, 
70, 
80, 
90, 

100, 


oOo ON SD 


times. 
times. 
times. 
times. 
times. 


a 


“16 DIVISION. 


LESSON XI. 
REVIEW LESSON. 


6 in 54, how many times/ 8 in 40, how pay times? | 
3 in 18, 4 in 36, 


| 4in 20, oak Tin 49, 6 
| 9 in 27, oe 4 in 16, as 
8 in 72, 7 in 28, st 
5 in BD; ff 8 in 64, 6 
9 in 81, rh 6 in 12, My 
6 in 18, i 9 in 63, e 
7 in 42, ss 5 in 2d, é 
| 8 in 16, how many times? 9 in 54, how many times? 
7 in 21, “6 3 i in 21, ps6 
| 3in 27, eS ra in 56, . 
7 in 63, « 8 in 48, “ 
5 in 40, 9 in 45, * 
9 in 18, Y 2 in 14, ms 
Bevaoe 5 gS '6 in 48, FF 
6 in 42, « 8 in 82, os 
yan £5, 277, 7°88 4 in bi = 


6 in 30, how many times ‘3 in 24, how many times? 
66 


9 in 36,: 2 in 16, 

5 in 380, cs 4 in 32, ¢ 
4 in 24, e 6 in 24, 
2in 6, . Tip uh 5 

7 in 14, a: 2 in 10, $$ 

5 in 10, A 5 in 20, A, 
7 in 35, pee 4in 8, S 


4 in 12, -yO1in 10, . o 


DIVISION. T% 


-—————$—$ eens 


LESSON XII. 
PROMISCUOUS QUESTIONS. 


r 1. Sarah learned 32 lessons in 8 days; how 

_many lessons did she learn each day ? 
| . If a horse travels 68 miles in 7 hours, how 
| many miles does he travel in one hour? 
| 3. If 9 men consume 81 pounds of bread in a 
week, how much would one man consume? 

4. How long will it take 6 men to do a piece of 
work, that one man can do in 48 days? 

5. If 90 bushels of apples will make 10 barrels 
of cider, how many bushels will make one barrel 
of cider? 
| 6. How long will it take a man to build 72 feet 

of wall, if he builds 9 feet a day ? 
| %. How long would it take a steamboat to go 
70 miles, at the rate of 10 miles an hour? 

8. How many sheep, at 3 dollars a head, can be 
| bought for 27 dollars? 
| 9. How long will 45 dollars pay for keeping a 
, horse, at the rate of 5 dollats a month? 

10. A boy divided 36 cents, equally, among 4 
beggars; how many cents did he give to each? 

11. At 6 cents a pound, how many pounds of 
rice can I buy for 42 cents? 

12. At 7 dollars a rod, how many rods of fence 
can be built for 49 dollars ? 


| 
| 
: 
| 


| 
} 
/ 


18 DIVISION. 


Se 


13. There are 7 days in a week; how many | 


weeks are there in 56 days? 

14. If 5 men can build a wall in 8 days, how 
long will it take 1 man to build it? 

15. If I pay 4 dollars for a ton of coal, how 
many tons can I buy for 382 dollars? 


16. If you have 72 pounds of butter, which you | 


wish to put in 9 sh ein how much must you put 
in each box? 


17. A farmer sold 8 cords of wood for 48 dol- | 


lars; how much did he receive a cord ? 


18. If a cabinet-maker sells 6 chairs for 54 dol- | 


lars, what would be the cost of 9 chairs ? 


19. If ten pounds of tea cost 60 shillings, what | 


will 5 pounds cost? 


20. If'4 men can hoe a field of corn in 3 days, | 


how long will it take 1 man to hoe it. 


21. Ifa boy travels 64 miles in 8 days, how far | 


will he travel in 5 days? 

22. Ifa piece of cloth containing 22 yards will 
make 11 coats, how many yards will it take to 
make 9 coats ? 

23. How many pounds of honey, at 9 cents a 
pound, can you buy for 108 cents ? 

24. What will 15 pounds of cheese cost, if 8 
pounds cost 40 cents? 

25. A grocer has 64 pounds of tea, which he 
wishes to put into parcels of 8 pounds each; how 


| many parcels will he have? | 


DIVISION. 79 


LESSON XIII. 


1. How many melons, at 6 cents apiece, will 
| pay for 9 oranges, at 4 cents apiece ? 


Awatysis.—WVine oranges, at 4 cents apiece, cost 
36 cents: As many melons can be bought for 36 
cents as 6 is contained times in 36: 6 in 36, 6 
times: Therefore, 6 melons, at 6 cents aprece, will 
pay for 9 oranges, at 4 cents aprece. 


2. Tow many yards of cloth, at 3 dollars a 
yard, can be bought for 4 barrels of flour, at 6 

| dollars a barrel? 

3. A grocer sold 9 pounds of tea, at 7 cents a 
pound, and took his pay in eggs, at 9 cents a 
dozen; how many dozen did he receive? 

| 4. Harry has lemons worth 4 cents apiece; how 
many must he give John for 2 quarts of cherries, 
| worth 8 cents a quart? 

| 5. William worked 6 days, at 10 cents a day, 
_ and took his pay in oranges, worth 3 cents apiece; 
how many did he receive? 

_ 6. If a family of 6 persons have provisions for | 
8 weeks, how long will it last 1 person ? 

7. A butcher sold a baker 9 pounds of beef, at 
5 cents a pound, and took his pay in bread, at 12 

| cents a loaf; how many loaves did he receive ? 

8. If 3 weeks’ board costs 18 dollars, what will 

| 9 weeks’ board cost, at the same rate? 


—_——— ——- 


80 DIVISION. 


9. How much sugar, at 9 cents a pound, must 
be given for 9 dozen of eggs, at 10 cents a dozen ¢ 
10. How many barrels of flour, at 8 dollars a | 
barrel, must be given for 10 sheep, at 4 dollars | 
apiece ¢ | 
11. How many yards of cloth, at 3 dollars a | 
yard, must be given for 6 calves, at 9 dollars | 
apiece ? | 
12. How many bushels of wheat, at 2 dollars a | 
bushel, must be given for 2 barrels of sugar, worth | 
16 dollars a barrel ? | 
13. A man wishes to exchange 20 sheep, worth | 

3 dollars apiece, for calves worth 5 dollars apiece; | 
how many calves should he receive? | 
14. If 2 apples are worth 10 chestnuts, bow 
| 

| 

| 

| 

{ 

| 

| 


many chestnuts will 20 apples buy ? 

15. Six lemons are worth 24 apples; how many 
lemons will 16 apples buy ? | 

16. How many yards of cloth, at 4 dollars a 
yard, can be bought for 12 calves, at 3 dollars 
apiece ¢ 

17. John wishes to exchange hens, worth 2 shil- | 
lings apiece, for 12 ducks, worth 3 shillings apiece; | 
how many hens must he give for the ducks ? | 

18. How many sheep, worth 4 dollars apiece, 
must be given for 6 calves, worth 6 dollars apiece ¢ 

19. A grocer sold 12 pounds of tea, at 6 shillings | 
a pound, vane took his pay in wheat,’at 9 shillings | 
a bushel; how many bushels did he receive? | 


FRACTIONS. 


LESSON I. 


_ 1. Ifanorange _ be divided into 
equal parts, each of the parts is called, one-half. 


2. Ifan orange be divided into 
equal parts, each of the parts is called, one-third. 


3. Ifan orange __ be divided into 
equal parts, each of the parts i&called, one-fourth. 


4. Ifan orange be divided into 
equal parts, each of the parts is called, one-fifth. 
| 5. If an orange be divided into 6 equal parts, 
each of the parts is called, one-siath. 
6. If an orange be divided into 7 equal parts, 
each of the parts is called, one-seventh. 
7. If an orange be divided into 8 equal parts, 
each of the parts is called, one-eighth. 
| 8. If an drange be divided into 9 equal parts, 
each of the parts is called, one-ninth. 


82 FRACTIONS. 


9. If an orange be divided into 10 equal parts, 
each of the parts is called, one-tenth. 

These equal parts of the orange, are called 
Fractions. They are thus written: 


One-half . 4 One-seventh . } 
One-third . t One-eighth _ 
One-fourth 1 One-ninth. a 
One-fifth . 1 One-tenth. wi 
One-sixth. . . §% | One-twelfth. . ;4 


The number above the line, is called the nwmer- 
ator; and the number below the line, is called 
the denominator. 

10. How many halves are there in one orange? 

How many thirds are there in one orange? 

How many fourths are there in one orange? 

How many fifths are there? How many sixths? | 

How many sevenths? How many eighths? 

How many ninths? How many tenths ? 

11. Which is the greater, one orange or one-half 
of an orange ? 

Which is the greater, one-half or one-third / 

Which is the greater, one-fourth or one-third ? 

Which is the greater, one-fourth or one-fifth ? 

Which is the greater, one-sixth or one-fifth ? 

Which is the greater, one-sixth or one-seventh ? 

Which is the greater, one-eighth of one-half? 

Which is the greater, one-third or one-tenth ? 


FRACTIONS. 


LESSON II. 


1. How many halves of one orange are there 
in two oranges ¢ 


Awnatysis.—ln 2 oranges, there are two times 
as many halves as in 1 orange ; in 1 orange there 
are 2 halves: Therefore, in 2 oranges there are two 
times 2 halves, or 4 halves. 

2. How many halves of one orange are there in 
3 oranges? How many in 4 oranges? In 5? 

3. How many halves of one orange are there in 
7 oranges? How many in 8 oranges? In 10? 


The halves are thus written: 


Two-halves . = Ten-halves . 32 
Three-halves . $ Twelve-halves - 42 
Four-halves . $ Sixteen-halves . 48 
Five-halves . 5 Kighteen-halves . 42 
Seven-halves. 5 | Twenty-halves . 2? 


. How many halves of 1 are there in 2? 
. How many halves of 1 are there in 6? In 7? 
. How many halves of 1 are therein 9% In 10? 

How many halves of 1 are there in 8? In 8% 
. How many halves of 1 are there in 5? In 4? 


COOnr DS Ot > 


84 


FRACTIONS. 


9. HLow many oranges are equal to 8 halves ? 


Awnaxysis.—Since 2 halves are equal to 1 orange, 
there will be as many oranges in 8 halves as 2 a8 
contained times in 8: 2 im 8, 4 times: Therefore, 
8 halves are equal to 4 oranges. 


. How many apples are equal to 2 halves? 

. How many apples are equal to 4 halves? 

. How many pears are equal to 8 halves? 

. How many melons are equal to 20 halves? 

. How many peaches are equal to 16 halves? 
. How many plums are equal to 18 halves? 

. How many plums are equal to 14 halves? 

. How many lemons are equal to 12 halves? - 
. How many lemons are equal to 18 halves? 
. How many pears are equal to 10 halves? 

. How many plums are equal to 8 halves? 

. How many units 1 are there in 6 halves? 

. How many units 1 are there in 12 halves? 
. How many units 1 are there in 14 halves? 
. How many units 1 are there in 18 halves? 
. How many units 1 are there in 20 halves? 
. How many units 1 are there in 16 halves? 

. How many units 1 are there in 18 halves? 
. How many units 1 are there in 6 halves? 

. How many units 1 are there in 2 halves? 


FRACTIONS. 


LESSON III. 


1. How many thirds of an orange are there 
in 4 oranges ? 


| Anatysis.—ln 4 oranges there are 4 times as 
many thirds as in 1 orange: in 1 orange there 
sare 3 thirds: Therefore, in 4 oranges there are 4 
| times 8 thirds, which are 12 thords. 


2. How many thirds of an orange are there 
in 2 oranges ? 

How many thirds are therein 3 oranges? In 4? 

'low many thirds of 1 are there in 2¢ In 6? 

[low many thirds of 1 are therein 4? In 5? 

3. How many whole oranges are equal to 9 
| thirds ¢ 
| Awatysis.—Since 8 thirds of an orange are 
| equal to 1 orange, there will be as many oranges 
in 9 thirds as 3 7s contained times in 9: 3 in 9, 
3 times: Therefore, 9 thirds are equal to 3 oranges. 


4. Flow many oranges are equal to 12 thirds? 
How many oranges are equal to 15 thirds? 
How many units 1 are equal to 21 thirds? 

5. How many units 1 are equal to 27 thirds? 
How many units 1 are there in 3 thirds? 
How many units 1 are there in 9 thirds? 


86 FRACTIONS. | 


LESSON IV. 


| 
| 
1. How many fourths of a lemon are there | 
in 3 lemons? | | 

/ 


Anatysis.—In 3 lemons there are 3 times as | 
many fourths as in 1 lemon: in 1 lemon there | 
are 4 fourths: Therefore, in 3 lemons there are 
3 times 4 fourths, which are 12 fourths. 


2. How many fourths of a lemon are there in | 
| 2 lemons ? In 3? In 4? | 
| How many fourths are there in 6 lemons? | 
| How many fourths of 1 are therein 5? In 7? | 
| 3. How many whole lemons are equal ‘to 8 | 
| fourths ? 

| Awnatysts.—Since 4 fourths of a lemon are 
equal to 1 lemon, there will be as many lemons 
an 8 fourths as 4 is contained times in 8: 4 m 8, 
2 times: Therefore, erght fourths are equal to 2 
lemons. 


4. How many lemons are equal to 12 fourths ¢ 
How many lemons are equal to 16 fourths ? 
How many lemons are equal to 32 fourths? 

5. How many lemons are equal to 36 fourths ! 
How many units 1 are equal to 4 fourths? 
How many units 1 are equal to 20 fourths ? 


FRACTIONS. 


LESSON V. 


1. How many fifths of an orange are there in 
2 oranges ¢ 


Anatysis.—Jn 2 oranges there are 2 times as 
many fifths as in 1 orange: in 1 orange there are 
5 fifths: Therefore, in 2 oranges there are 2 times 
5 fifths, which are 10 fifths. 


How many fifths of 1 are there in 3? In 4? 
How many fifths of 1 are therein 52 In 6? 
2. How many units 1 are there in 20 fifths? 


Awnatysis.—ZIn 1 there are 5 fifths: in 20 fifths 
there are as many units 1 as 5 is contained times 
in 20: 5 in 20, 4 times: Therefore, there are 4 
units 1 in 20 fifths. 


3. How many units 1, in 45 fifths? In 60 fifths? 
4, How many fifths of 1, in 6? In 7? In 8? 
5. How many sixths of an orange are there in 
2 oranges? In4? In 5! 
How many sixths of 1, in 2? How many in 3? 
How many. oranges are equal to 24 sixths? 
How many units 1, in 36 sixths? In 42 sixths? 
How many units 1, in 48 sixths? In 54 sixths? 
How many sixths of 1,in 12% In 8? In 9? 
How many sixths are there in 7¢ In 12% 


88 - FRACTIONS. 


6. How many sevenths of an orange are there 
in 3 oranges ? 

How many sevenths of 1,in3? In7? In 9? 

How many sevenths of 1, in 4? In 5? In 8? 

How many oranges are equal to 21 sevenths? ° 

How many units | are there in 21 sevenths? 

How many units 1, in 35 sevenths ? 

7. How many eighths of an orange are there 
in 2 oranges ? 

How many eighths of 1 are there in 2? In 3? 

How many eighths of 1 are therein 4? In 5? 

How many oranges are equal to 24 eighths? 

How many units 1,in 24 eighths? In 40 eighths? 

8. How many ninths of an orange are there 
in 3 oranges ? 

How many ninths of 1 are there in 3? 

How many ninths of 1 are there in 4? In 5? 

How many oranges are equal to 18 ninths ? 

How many oranges are equal to 27 ninths? 

How mé@ny units 1 are equal to 36 ninths? 

9. How many tenths of an orange are there 
in 2 oranges? 

How many tenths of 1 are there in 3? In 4? 

How many tenths of 1 are there in 5? In 6? 

How many tenths of 1 are therein 7? In 8? 

How many oranges are equal to 30 tenths? 

How many units 1 are equal to 40 tenths? 
How many units 1 are equal to 60 tenths? 
How many units 1 are equal to 70 tenths? 


FRACTIONS. 89 


LESSON VI. 


1. If 1 pound of tea costs one-half of a dollar, 
what will 4 pounds cost? 


Anatysis.—four pounds of tea will eost 4 times 
| as much as1 pound. Since 1 pound costs one-half 

of a dollar, 4 pounds will cost 4 half-dollars, 
which are equal to 2 dollars: Therefore, if one 
pound of tea costs oa a dollar, 4 Bowness, will 
cost 2 dollars. 


2. If a bushel of apples costs one-third of a dol- 
lar, what will 9 bushels cost é 

3. If John pays one-fourth of a dollar for a pen- 
knife, how much must he pay for 8 penknives, at 
the same rate? 

4. If a yard of calico costs one-fifth of a dollar, 
how much will 20 yards cost? 

5. What will 8 barrels of flour cost, if one-sixth 
of a barrel costs 2 dollars ? c 

6. If 1 pound of sugar costs one-eighth of a 
ran what will 16 pounds cost 

sale one-ninth of a piece of cloth contains 5 


yaaa how many yards are there in the whole. 


pr 
_ If 1 bushel of wheat costs one-tenth of a dol- 
ms what will be the cost of 40 bushels? 
9. If a bushel of corn costs one-fifth of a dollar, 
what will be the cost of 15 bushels? 


3 


Sa a 


——— 


| 90 } FRACTIONS. 


10. If half an ox is valued at 50 dollars, what 
is the value of the ox? 

11. If one-fourth of a bushel of peaches costs 4 
shillings, how many shillings will 2 bushels cost ? 

12. If a man earns 3 dollars in one-fifth of a 
month, how much will he earn in 2 months? 

13. If one-seventh of a yard of silk costs 10 
cents, how much is that a yard ? 

14. If one-eighth of a pound of tea costs 7 cents, 
how much is that a pound? 


yards, how many yards are there in the piece ? 

16. If a man earns 8 dollars in one-tenth of a 
month, how much will he earn in 2 months? 

17. If one-fifth of a barrel of flour lasts a family 
8 days, how long will 2 barrels last them ? 

18. If one-third of a cheese is worth 2 dollars, 
what is the value of the whole cheese ? 

19. If one-eighth of a barrel of apples is worth 2 
shillings, how many shillings are 3 barrels worth ¢ 
- 20. If in one-tenth of a month, a man earns 2 
dollars, how much ean he earn in 8 months ? 

21. If two cents pays for one-eighth of a melon, 
how many cents will buy-2 melons? 

22. If 3 cents pays for one-fourth of a dozen of 
eggs, what will 4 dozen cost? 

23. If one-ninth of a piece of cloth contains 5 
yards, how many yards will 4 pieces of the same 
| length contain 


Fe ee ee ee i oe 


15. If one-eighth of a piece of cloth contains 4 | 


| 


q 


$1 = 100 cents. 


1 
4 


UNITS OF ARITHMETIC. 


91 | 


Uwirs or Apstract NuMBERS. 
10 units make 


10 tens 


10 hundreds . 


UNITS OF 


1 ten. 
1 hundred. 
1 thousand. 


The abstract units are, 1, 10, 100, 1,000, d&e. 


CURRENCY. 


Unirep Stares Money. 


10 mills make 
BOs cenis (.:°: 
1@ dimes . 
10 dollars . 
20 dollars 


4 of a dollar = 
1 of a dollar = 
1 of a dollar = 
1 of a dollar = 


Ewauisu Srertinc Money. 


5 


2 


e 


0 


2 


4 farthings make . 


12 pence. . 
20 shillings . 
21 shillings 


a 


ae 


4s 


- 


i 
s 


1 
2 


1 cent, . 
1 dime, . 
1 dollar, 
1 eagle, 


7 


. . . 1 double eagle, D. #. 
The units of this currency are, 1 mill, 1 cent, 1 dime, 
1 dollar, and 1 eagle. 


of a dollar = 122 cents, 
zs of adollar = 10 
ys of a dollar = 61 
so Ofadollar= 5 * 


of a cent 


1 penny, . 
1 shilling, 
1 pound, . 
1 guinea, 


es 
—- 


2 


2 


5 mills, | 


-—< 


The units of this currency are, 1 farthing, 1 penny, 
shilling, 1 pound, and 1 guinea. | 


| 92 


UNITS OF 


ARITHMETIC. 


Units or Lenornu. 
Linear Merasure. 


12 inches, in. make 
3 feet. oarie% ; 
54 yards, or 164 feet . 
40 rods 


8 rniles . 


statute miles. 


8 furlongs, or 820 rods. 


geographical, or 693 


e 


ty 


k: f00t 4) Jo pene ast 
Yyard,.. ‘¢.aeiwie@ ated. 
h POG ei oth pditaecey es 
1 furlong, . . . 7. far. 
PRONG. Uk niente ioe ae ais 
Pdeacud, Bosse lena ede 


. deg. or °. 


degree, . 


What are the units of this measure ? 


Crotn MErasure. 


27 inches, im. make . 
ATONE oa iS 


a QuaCibTS, js.) t. le yard 7. tal @ 8. boat 
S quarters, . .. . 1 Ell Flemish, . £4. F7. 
SB UATIORS 2 eu” . 1 El) English, . #B 
What are the units of this measure? 
Univs or SURFACE. 
SquaRE Muasure. 
144 square inches, sg.ia. make 1 square foot, . ag. ft. | 
9.-square feet)... - 1 square yard, . sq. yd. 
30} square yards. . « 1 squarerod; 2. P. 
40."square reds i=") is 2. 2 reed, 2 set) 2 RB. 
A: OOS) 2 MEE OS PL are 
GtGrcacres eye Pr) cha eeiguare miley mere AP. 
What are the units of this measure ? ; 


Pnail 2 Se ee 
1 quarter of a yard, qr. 


[(———-——- 


/ UNITS OF ARITHMETIC. 93 
Units oF VOLUME. 
Supic MEASURE. 


1728 cubic inches, cv.in. make 1 cubic foot, . cu. ft. 
27 cubic feet 2° i. . . 1 eubie yard, ’aicu. yd. 
40 feet of round, or ) 


50 feet of hewn timber § 1100; ey rate Bi 


42 cubic feet . . . . . 1 tonofshipping,. 7. 
16 cubic feet “SH Lore! J* cord footy err Fe fh 
8 cord feet, or } 
128 eubic feet J ° 
What are the units of this measure? 


be bords. tS eee 


Liguip MEASURE. 


4 gills, gi:make . . . 1 pint, . . . pt. 
| 2 pints L*quart, .) . 496 
4 quarts , 3 Vegallon, 9... aregars 
Po old pallots; 2 4... «1 barrely sr bar. 
| 63 gallons 1 hogshead,. . hhd. 
| 2 hogsheads L pipe; 2.) Ge pte 
2 pipes, or 4 hogsheads 1 tun,. . «. « tum. 
What are the units of this measure? 


Dry Measure. 


2 pints, pt. make. . . 1 quart, . . . gt. 
Sequarta... .. jyeteedy 3 2 peck. 5) jedunwt ae 
4 pecks . . . . ~~ 1 bushel,. . . bu. 
$6) buabelé...vutsees 4. 1 chaldron, sumo eke 


What are the units of this measure? 


94 UNITS OF ARITHMETIC. 


Sw 


Units or WerIGut. 


Avorrpuprors Wricurt. 


hGncrams, dz wmaks» ..1..%. 1] ounce... 5 aii Ome 
EG LOUNCES adie bo A PORN, nnd ce 
mo POURS fe PW eB GATE eek a ee 
4 quarters . . ... . 1 hundredweight, cwt. 
20 “hundipdweighh..ps. . BytODy 6 saeenten te 
What are the units of this weight? 


Troy Weieut. 


- 20 pennyweights . ./ 1 ounce, . . O28, 
E22 OUNCES s. 0! (eee Eee eae, ~~ os abe 
’ 


APporTHoecaARins’ Wrigut. 


20 “wramseor. make . ¢. ‘1 serapley .. 3 
| Boecraplea”. 20ers. eng) 1 rams. 
MEOFOINS: i, ah ie, kee TOU DOR, 
12eannees. |. 34. £2) 2 1 pound, 


ape. SO 


Units or Time. 


60 seconds, sec. make . 1 minute,. . . ™. 
GOomimtes oe.fes/ eas ew 2) Wate . . aeaiee er, 
Sdohonts. praat ete 1: CY ice! ihe ern omae 
Ty Gage ae" a st? AMO > L oweekyg., 4, un gee. 
weeks +. .e Piet oo. Lomonthy .. Baca. 
bg eee PET Ts oad SOE, 2 og, ae eee as | 
100 years... 1 @entury;. aoe | 


\ What are the init of time ? “s | 


| 
24 grains, gr. make . . 1 RAnAY SineAh put. 
| 
| 
| 
| 


a 


UNITS OF ARITHMETIC. 95 | 


Ture YEAR. 


Winrek, 4 1 month, January,, 31 days. 


2  “ February, 28, in leap-year, 29. | 
3 “March, 31 days. } | 
SPRING, 4: seo gw Api), 20.;, 4 
5st May, Sioa 
( 6 Ayh*> vdane, BOs ae 
Summer, { 7 ee daly, si + 
/ 8 . August, hme 
a. & ipepeamben, 30° |S 
Autumn, < 10 
11 “ November, 30 “ 
Winter, 12 “ December, 31 ¢ 
There are, inthe year, . . 365 days. 
Unirs or Crrcutar Measure. 
60 seconds, ’’ make . . 1 minute, « 


60 minutes . .. . . 1 degree, 
30<degregas. «2 =a» 1. SIGN, .<. <galiontee (Bp 
12 signs, or 360° . . . 1 circle, . 


Reig MisceLuANneous TABLe. 


12 units, or things, make . 1 dozen. 
Pai dogem yon, (ay tiods, papl! gross 
12 gross, or 144 dozen . 
20 things score, 


1 great gross. 

] 
196 pounds . . . . . . 1 barrel of flour. 

1 

1 


| 
i 
“ October, 31 “ 
} 


24 sheets of paper ; quire. 
ream. 


40 qhinty, Goes): AA 2 
fe SRR yer CONE. 


—— 


Fectly learned by every pupil. 


96 


UNITS OF ARITHMETIC. 


MULTIPLICATION TABLE. 


The Multiplication Table, as far‘as 12, should be per- 


Every combination should 


be so familiar as to be made without the least hesitation 


or delay. 


The time and labor, necessary to accomplish 


this most desirable object, should be cheerfully bestowed, 


both by teacher and pupil. 


1/ 2 7 51 6 g| 9 10/11 12 
9] 4] 6| 8110/12/14] 16/18] 20/ 92] 24) 
~3l 6! 9/12! 15| 18/21/2941 27/ 30/ 33| 36 
wane 20/94/98! 32| 36] 40| 44| 48 
~ 5110/15 | 20| 95/30] 35| 401 45/| 50| 55| 60 
6119] 18/ 24/ 30/36/42) 48| 54/ 60! 66! 79 
4 14 35| 42| 49156) 63| 70| 77/84 
8116] 24/1 32| 40/| 48| 56| 64| 72| 80| 88/ 96 
gf 1s} 97/361 45/ 54/631 72/ 811 90/99 108 
10/20/30) 40/50) 60| 70 | $0| 90/100 |110/120 
11 | 92| 33 / 44/55 | 66| 77 | 88! 99/110 121 [139 | 
Gcrtaointsinaerat 


Find from the table, the product of 8 by 7? 9 by 12? | 


Find ides Sioa dite by 112, 11 by 9? a Mame F | 


READING FIGURES. 97 


READING FIGURES. 
a 


LESSON I. 
SUGGESTIONS. 


Pourizs, in Arithmetic, should be taught, from the very 
commencement, to read the figures. By reading, we mean 
the use of those words only which declare the final results. 

For example, 2 and 2 are 4. The word, four names 

the result arising from adding 2 and 2 together; we 
generally spell this word by saying, two and éwo, are four. 
The pupil should be taught to read, and say, four. 

Hence, after having taught the combinations in addi- | 
tion, in the usual way, as 1 and 1 are two; 1 and 2 
are three, &c., let each set of combinations be written 
separately on the blackboard, as on the following page. 

Let the teacher then take a pointer, and beginning at 
the right hand, point to the figures 1 and 0, and let the 
whole class answer, one. Let him then point to the 
figures 1 and 1, and let the class answer, éwo ; and so 
on, for the entire table. Let each set of combinations 
be read in the same manner. 

This reading will save the use of four words in each 
combination. Thus, instead of saying 1 and 6 are 
seven, the eye glances at 1 and 6, and seven is uttered 
immediately. The drill of the class should be continued 
until all the combinations can be read by the eye. Let 
each of the ten sets be taught in the same manner—and 
thoroughly taught. Let similar readings be made in 
Subtraction, Multiplication, and Division. 


98 


[om low lato [mao |ro [Ro [wo [POO [RO 


IS 


READING FIGURBES. 


8 
1 


tom fam [rma [mm [Rw Two |rwow 


[<> aw 


LESSON II. 
READING AS FAR 5. TWENTY. 
rol gs Ube nee ee 
Icgh pod pal) 
DR honey ek: 
2 2 2 2 2 
i. § ee Epes 
Sl BS et ier nD 
a Ceo Si: 
ee eee 
PR i ae 
Fis Bi, Achaea ae 
vi i eS a ae | 3 
bie 06 6 eb 
Bs. gre Sh? 4 PORBG 
ge MR ONES OGD D 
tiie 6) en 
aa ris fe 
een age Pay APE 
Bs eee aBicee Niheee 
ORG. By wk. ee 
10 10 10 10 10 


S 
oo 


| = dO 


Teh. eee Miewe nay So eae et ee ee trae | ae 


READING FIGURES. 99 


LESSON ITI. 


READING WITH THE LARGER NUMBERS. 


lg A ae ile Sl ae Ss a ae 
m 1 10 16 1 1 10 40 10 M 

a Ome. eT SA ah et 8 8 OO 

(/ie Wh it bb. Wk he Ie lb 12 Maa 

| + ta ea wie a3 

| 


AS es Sa ts aE Se a ae 
Mois 12 12 12 Bb 2b Bb Ye 


gee he ey Ed ehitd geo ty 
18 13 18 18 13 18 18 13 13 18 18 


ee eee ae 4 3 Rg 
eta: S14 Lg se 


Be iy St Ss ee SS Se 
Boye loro 1b 1S 15. 15) SaaS 


o Feet, Mow oO. 4°, ee ae 
SiG ator etO mGomlg 1G hep lé 


Pao" oS YS SY FE THEM 8S tg eee 
Beh. 20) OPUS as RG Os 


PO 49° 9S SR 26. ch 14> 78s 480d 
| 18 18 18 18 18 18 18 18 18 18 18 


ro), Gee (ah stay, a eee kee Le 
ae 192 TS TOD OT YQ FOP PE ge ay 


——— _— —_—, ee ee ee —_—— _ — —— 


100 READING FIGURES. 


LES SOW aby. 


READING BY THE EYE ABOVE TWENTY. 


By 9 BURT) 6 REP BA RY BES 0 
20 20 20 20 20 20 20 20 20 20 20 


3 
ining Sai: UR 3 Wi? eS UR) MS) 


SO A ae ee MS ee 
Be 24 R494 Od Gd od Bd ok ae 
Pee ee a Ta Se Ss aT 
BE 8S APE IP 20) 088. Uy SANA SE 
LORS aia Qe Mare Gerrit, ia) 
26 26 26 26 26 26 26 26 26 26 26 
bil eM se SMies aie kei cet 
oe ie a Mm oe ame Py br 
27° 97.907 BT OT 97.0% ATi eT oat 


ges Let the Teacher writé, in succession, on the | 
blackboard, all the numbers to 100, in sets of ten, and | 
exercise the class in the readings. | 


READING FIGURES. 101 


ee 


LESSON V. | 
READING COLUMNS OF THE SAME FIGURES. 
Rae ae Be Gta att ER 
beose 8 4 EBS oT) 8 Se 
repose Ss (84 Se OB) TTR) gs C819 Stee 
Reeth 6c BS Ge Ay. - 8 oy Gem | 
Pesiy Sat, cb: Gy Tie Briel 
pene 7 84 OG Ge: Teg cere 
fee 8 04 oS lg 8h e 4tO 
fees Sua 5 BR. te Se yO arO 
ey SPOS Be DT 4 Bi BRIO 
Mee e384 Bb Be ay 8b 8 oO 


Ten times 1, are how many? ‘Ten times 2, are how 
nany? Ten times 3? Ten times 4? Ten times 5? 
[en times 6? Ten times 7? Ten times 8? Ten 
jimes 9? Ten times 10? | 


Read the following : 


1 
2 
3 
0 
1 
3 
I 
4 
3 


| > 00 Hm Fe co bo Or 9 
JOR OOD We bo 
LAN RAR OTaRaHO 
i>TWOWHDH OD 
jer OH RH Oo H-TO OH HT 
|; PLL HOF, OOS 
|lOomorFNonwor 
Pe 
|oOoOHONWWaAS?D 


102 READING FIGURES. 


LESSON 


‘EXAMPLES IN READING 
2) ie (BPP A Te) 
0 5 " 3 1 
1 4 HoT A u0e ” 2.0 
Bu O08, 80 A dias 
4 1 9 Yam .9 
8 7 1 5 7 
0 8 6 6-6 6 
i. FAD 8 3 
ie Be mac On tae 
Hee 3 0 1 4 
Buia ob st 3 9 


ae 


LONG 


(6) 


JR DOWArTOONO-T 


COLUMNS, 


Cid (8) 
Git 9 
94%.58 
Saket 
ee 
Tin ty 9 
6 0 
lia. "9 
Sy ge 
re 
alt uae 


IS 


READING FIGURES. 


LESSON VIT. 


READING IN SUBTRACTION. 


8 7 6 5 4 3 
1 1 ] 1 1 1 
9 8 7 6 5 4 
2 3 yy 2 2 2 
10 9 8 7 6 5 
CES et oan CAC 
LL> iu 9 8 T 6 
4 1m GC 4 4 4 
LS jth lO 9 8 yf 
Bini ve Shing Re to 
bY eee i a 9 8 
6 6 6 6 6 
ahiincdnie a Adee: a 
Tt to, Lame 1. hee eo 
1 AM 7 A 7 qT 
L600 14 -- 43. | 4 
8 8 8 8 8 8 


[woo jaw faa [aw [eo [om roc [eno 


pias 
oS = 


Bs 


1038 


v 


1. 
2. 


t= OO 


“I co Gn 


—" 
he OO Nar 6 "00 


qn 


oF 


—" 
m™ GH pom © SS @ eat 


ora! 


the other numbers, as far as 10. 


READING FIGURES. 


LESSON VIII. 


COUNTING BY THE NUMBERS FROM 1 To 1QO. 


Count by the one’s to 50. How many 1’s are there? 


Count by the 2’s to 50. 
. Count by the 3’s to 51. 
. Count by the 4’s to 52. 
. Count by the 5’s to 50. 
. Count by the 6’s to 54. 
. Count by the 7T’s to 56. 
. Count by the 8’s to 56. 
. Count by the 9’s to 54. 
. Count by the 10’s to 50. 


. Subtract 1 from each number, from 50 to 1. 

. Subtract 2 from 50, and then from each remainder. 
. Subtract 3 from 51, and then from each remainder. 
. Subtract 4 from 52, and then from each remainder. 
. Sabtract 5 from 50, and then from each remainder. 
. Subtract 6 from 54, and then from each remainder. | 
. Subtract T from 56, and then from each remainder. 
. Subtract 8 from 56, and then from each remainder. 
. Subtract 9 from 54, and then from each remainder. 
. Subtract 10 from 50, and then from each remainder. 


. Add 1 to 50, and to the sum, as far as 100, 
. Add 2 to 50, and to the sum, as far as 100. 
. Add 3 to 50, and to the sum, as far as 100. 
. Subtract 1 from each number from 100 down to 50. 
. Subtract 2 from each number from 100 down to 50. 
. Subtract 3 from each number from 100 down to 50. 


ik 


How many 2’s are there? 
How many 3’s are there? 
How many 4’s are there? 
How many 5’s are there? 
How many 6’s are there? 
How many 7’s are there? 
How many 8’s are there? 
How many 9’s are there? 
How inany 10’s are there? 


Do the same in addition and subtraction, for each of 


READING FIGURES. 105 


LESSON IX. 


MULTIPLICATION BY THE EYE. 


SS Bee. Sey eee ee: ee eae 


eee 


Hh aS | Si SRR: TS SS FP A AE 


nm ee 


eee ows Ce CO. ae a ae Ze 


me 


Ro Ce ee epee OO EES Read 


mm eee 


0 
0 
2 
0 
3 
a 
4 
0 
fie 
0 
ite 
0 
ah 
0 
8 
0 
iD 
0 
10 


106 READING FIGURES. 


———— a 


LESSON X. 


DIVISTON BY THE 2k YE. 


Le : Se: a See ae ORR pa eee 


ts 8 Bee. 19 ae tee 


B23 OWN 12 We 18-81 4 Oy BO 


W)4 OB 18" 16) 20) 24 28 82) Sh cad 


By Googe) By 867.46 . 54 163) 128 Seee 


10)10 20 30 40 50 60 70 80 90 100 


Gu (ay (8) (4) (5) (6) |e 
2)24 2)36 2) 1938. 2)428 2) 362 2) 486 | | 


Bee ety ode GD). agg GAO) ans 
4)86 8) 126 8) 96 8)42 8) 25a 


(12) (13) (14) (15) (16) 
448 4)28 4) 2484) B44) 16 


f 


(1) 
1) 61 


(6) 
2) 16 


(iL) 
5) 21 


(16) 
4) 124 


(20) - 
Bah) 105 


(24) 
6) 216 


(28) 
v)an7 


(32) 
8) 968 


(36) 
9) 819 


READING FIGURES. 


LESSON XI. 


DIVISION BY THE EYE. 


(2) (3) (4) 
1) 45 1) 28 1) 29 


(9) 
2) 86 


(14) 
3) 672 


(7) 


(8) 
Hie 


(13) 
#) 129 


(12) 
3) 66 


(18) 


(17) 
5 4) 484 


(22) 
5) 360 


(26) 
6 ) 504 


(30) 


7) 966 __ 
PB. 


(34) 
8) 728 


(38) 
9) 459 


(5) 
1) 40 


(10) 
2) 90 


(15) 
3) 201 


(19) 
+) 368 


(23) 
5) 215 


(27) 
6) 954 


ya 
—T) 815 


(35) 
8) 488 


(39) 
9) 648 


